Numerical Integration of Stiff System of Ordinary Differential ...

African Journals Online (AJOL)

The goal of this work is to develop, analyse and implement a K-step Implicit Rational Runge-Kutta schemes for Integration of Stiff system of Ordinary differential Equations. Its development adopted Taylor and Binomial series expansion Techniques to generate its parameters. The analysis of its basic properties adopted ...

Comparative numerical solutions of stiff Ordinary differential equations using magnus series expansion method

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SURE KÖME

2014-12-01

Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.

Relationship between Static Stiffness and Modal Stiffness of Structures

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Tianjian Ji Tianjian Ji

2010-02-01

Full Text Available This paper derives the relationship between the static stiffness and modal stiffness of a structure. The static stiffness and modal stiffness are two important concepts in both structural statics and dynamics. Although both stiffnesses indicate the capacity of the structure to resist deformation, they are obtained using different methods. The former is calculated by solving the equations of equilibrium and the latter can be obtained by solving an eigenvalue problem. A mathematical relationship between the two stiffnesses was derived based on the definitions of two stiffnesses. This relationship was applicable to a linear system and the derivation of relationships does not reveal any other limitations. Verification of the relationship was given by using several examples. The relationship between the two stiffnesses demonstrated that the modal stiffness of the fundamental mode was always larger than the static stiffness of a structure if the critical point and the maximum mode value are at the same node, i.e. for simply supported beam and seven storeys building are 1.5% and 15% respectively. The relationship could be applied into real structures, where the greater the number of modes being considered, the smaller the difference between the modal stiffness and the static stiffness of a structure.

Substrate Stiffness Controls Osteoblastic and Chondrocytic Differentiation of Mesenchymal Stem Cells without Exogenous Stimuli.

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Rene Olivares-Navarrete

Full Text Available Stem cell fate has been linked to the mechanical properties of their underlying substrate, affecting mechanoreceptors and ultimately leading to downstream biological response. Studies have used polymers to mimic the stiffness of extracellular matrix as well as of individual tissues and shown mesenchymal stem cells (MSCs could be directed along specific lineages. In this study, we examined the role of stiffness in MSC differentiation to two closely related cell phenotypes: osteoblast and chondrocyte. We prepared four methyl acrylate/methyl methacrylate (MA/MMA polymer surfaces with elastic moduli ranging from 0.1 MPa to 310 MPa by altering monomer concentration. MSCs were cultured in media without exogenous growth factors and their biological responses were compared to committed chondrocytes and osteoblasts. Both chondrogenic and osteogenic markers were elevated when MSCs were grown on substrates with stiffness <10 MPa. Like chondrocytes, MSCs on lower stiffness substrates showed elevated expression of ACAN, SOX9, and COL2 and proteoglycan content; COMP was elevated in MSCs but reduced in chondrocytes. Substrate stiffness altered levels of RUNX2 mRNA, alkaline phosphatase specific activity, osteocalcin, and osteoprotegerin in osteoblasts, decreasing levels on the least stiff substrate. Expression of integrin subunits α1, α2, α5, αv, β1, and β3 changed in a stiffness- and cell type-dependent manner. Silencing of integrin subunit beta 1 (ITGB1 in MSCs abolished both osteoblastic and chondrogenic differentiation in response to substrate stiffness. Our results suggest that substrate stiffness is an important mediator of osteoblastic and chondrogenic differentiation, and integrin β1 plays a pivotal role in this process.

Stiff modes in spinvalve simulations with OOMMF

Energy Technology Data Exchange (ETDEWEB)

Mitropoulos, Spyridon [Department of Computer and Informatics Engineering, TEI of Eastern Macedonia and Thrace, Kavala (Greece); Tsiantos, Vassilis, E-mail: tsianto@teikav.edu.gr [Department of Electrical Engineering, TEI of Eastern Macedonia and Thrace, Kavala, 65404 Greece (Greece); Ovaliadis, Kyriakos [Department of Electrical Engineering, TEI of Eastern Macedonia and Thrace, Kavala, 65404 Greece (Greece); Kechrakos, Dimitris [Department of Education, ASPETE, Heraklion, Athens (Greece); Donahue, Michael [Applied and Computational Mathematics Division, NIST, Gaithersburg, MD (United States)

2016-04-01

Micromagnetic simulations are an important tool for the investigation of magnetic materials. Micromagnetic software uses various techniques to solve differential equations, partial or ordinary, involved in the dynamic simulations. Euler, Runge-Kutta, Adams, and BDF (Backward Differentiation Formulae) are some of the methods used for this purpose. In this paper, spinvalve simulations are investigated. Evidence is presented showing that these systems have stiff modes, and that implicit methods such as BDF are more effective than explicit methods in such cases.

Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems

International Nuclear Information System (INIS)

Hykes, J. M.; Ferrer, R. M.

2013-01-01

The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is 98 Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)

Free vibration of functionally graded beams and frameworks using the dynamic stiffness method

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Banerjee, J. R.; Ananthapuvirajah, A.

2018-05-01

The free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of the dynamic stiffness matrix in explicit algebraic form. The usually adopted rule that the material properties of the FGB vary continuously through the thickness according to a power law forms the fundamental basis of the governing differential equations of motion in free vibration. The differential equations are solved in closed analytical form when the free vibratory motion is harmonic. The dynamic stiffness matrix is then formulated by relating the amplitudes of forces to those of the displacements at the two ends of the beam. Next, the explicit algebraic expressions for the dynamic stiffness elements are derived with the help of symbolic computation. Finally the Wittrick-Williams algorithm is applied as solution technique to solve the free vibration problems of FGBs with uniform cross-section, stepped FGBs and frameworks consisting of FGBs. Some numerical results are validated against published results, but in the absence of published results for frameworks containing FGBs, consistency checks on the reliability of results are performed. The paper closes with discussion of results and conclusions.

PDASAC, Partial Differential Sensitivity Analysis of Stiff System

International Nuclear Information System (INIS)

Caracotsios, M.; Stewart, W.E.

2001-01-01

1 - Description of program or function: PDASAC solves stiff, nonlinear initial-boundary-value problems in a timelike dimension t and a space dimension x. Plane, circular cylindrical or spherical boundaries can be handled. Mixed-order systems of partial differential and algebraic equations can be analyzed with members of order or 0 or 1 in t, 0, 1 or 2 in x. Parametric sensitivities of the calculated states are computed simultaneously on request, via the Jacobian of the state equations. Initial and boundary conditions are efficiently reconciled. Local error control (in the max-norm or the 2-norm) is provided for the state vector and can include the parametric sensitivities if desired. 2 - Method of solution: The method of lines is used, with a user- selected x-grid and a minimum-bandwidth finite-difference approximations of the x-derivatives. Starting conditions are reconciled with a damped Newton algorithm adapted from Bain and Stewart (1991). Initial step selection is done by the first-order algorithms of Shampine (1987), extended here to differential- algebraic equation systems. The solution is continued with the DASSL predictor-corrector algorithm (Petzold 1983, Brenan et al. 1989) with the initial acceleration phase deleted and with row scaling of the Jacobian added. The predictor and corrector are expressed in divided-difference form, with the fixed-leading-coefficient form of corrector (Jackson and Sacks-Davis 1989; Brenan et al. 1989). Weights for the error tests are updated in each step with the user's tolerances at the predicted state. Sensitivity analysis is performed directly on the corrector equations of Caracotsios and Stewart (1985) and is extended here to the initialization when needed. 3 - Restrictions on the complexity of the problem: This algorithm, like DASSL, performs well on differential-algebraic equation systems of index 0 and 1 but not on higher-index systems; see Brenan et al. (1989). The user assigned the work array lengths and the output

Regulation of proximal tubular cell differentiation and proliferation in primary culture by matrix stiffness and ECM components.

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Chen, Wan-Chun; Lin, Hsi-Hui; Tang, Ming-Jer

2014-09-15

To explore whether matrix stiffness affects cell differentiation, proliferation, and transforming growth factor (TGF)-β1-induced epithelial-mesenchymal transition (EMT) in primary cultures of mouse proximal tubular epithelial cells (mPTECs), we used a soft matrix made from monomeric collagen type I-coated polyacrylamide gel or matrigel (MG). Both kinds of soft matrix benefited primary mPTECs to retain tubular-like morphology with differentiation and growth arrest and to evade TGF-β1-induced EMT. However, the potent effect of MG on mPTEC differentiation was suppressed by glutaraldehyde-induced cross-linking and subsequently stiffening MG or by an increasing ratio of collagen in the soft mixed gel. Culture media supplemented with MG also helped mPTECs to retain tubular-like morphology and a differentiated phenotype on stiff culture dishes as soft MG did. We further found that the protein level and activity of ERK were scaled with the matrix stiffness. U-0126, a MEK inhibitor, abolished the stiff matrix-induced dedifferentiation and proliferation. These data suggest that the ERK signaling pathway plays a vital role in matrix stiffness-regulated cell growth and differentiation. Taken together, both compliant property and specific MG signals from the matrix are required for the regulation of epithelial differentiation and proliferation. This study provides a basic understanding of how physical and chemical cues derived from the extracellular matrix regulate the physiological function of proximal tubules and the pathological development of renal fibrosis. Copyright © 2014 the American Physiological Society.

Applying homotopy analysis method for solving differential-difference equation

International Nuclear Information System (INIS)

Wang Zhen; Zou Li; Zhang Hongqing

2007-01-01

In this Letter, we apply the homotopy analysis method to solving the differential-difference equations. A simple but typical example is applied to illustrate the validity and the great potential of the generalized homotopy analysis method in solving differential-difference equation. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the differential-difference equations

Parallel Algorithm Solves Coupled Differential Equations

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Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Critical appraisal of the differential effects of antihypertensive agents on arterial stiffness

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Francesca Kum

2010-06-01

Full Text Available Francesca Kum, Janaka KarallieddeUnit for Metabolic Medicine, Cardiovascular Division, Kings College-Waterloo Campus, King’s College London, United KingdomAbstract: Increased central arterial stiffness, involving accelerated vascular ageing of the aorta, is a powerful and independent risk factor for early mortality and provides prognostic information above and beyond traditional risk factors for cardiovascular disease (CVD. Central arterial stiffness is an important determinant of pulse pressure; therefore, any pathological increase may result in left ventricular hypertrophy and impaired coronary perfusion. Central artery stiffness can be assessed noninvasively by measurement of aortic pulse wave velocity, which is the gold standard for measurement of arterial stiffness. Earlier, it was believed that changes in arterial stiffness, which are primarily influenced by long-term pressure-dependent structural changes, may be slowed but not reversed by pharmacotherapy. Recent studies with drugs that inhibit the renin–angiotensin–aldosterone system, advanced glycation end products crosslink breakers, and endothelin antagonists suggest that blood pressure (BP-independent reduction and reversal of arterial stiffness are feasible. We review the recent literature on the differential effect of antihypertensive agents either as monotherapy or combination therapy on arterial stiffness. Arterial stiffness is an emerging therapeutic target for CVD risk reduction; however, further clinical trials are required to confirm whether BP-independent changes in arterial stiffness directly translate to a reduction in CVD events.Keywords: aortic pulse wave velocity, augmentation index, blood pressure, renin–angiotensin–aldosterone system

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer

Numerical methods for the solution of ordinary differential equations

International Nuclear Information System (INIS)

Azeem, M.

1999-01-01

The ode 113 code solves non-stiff differential equations and is a fully variable step, variable order, PECE implementation in terms of modified divided differences of Adams-Bashforth-Moulton family of formulas of order 1-12. The main objectives of this project were to modify PECE mode of ode 113 into PEC mode, study the variable step size and variable order strategy of both the modes and finally, develop the switching strategy between both PECE and PEC modes to minimize the cost of solving the ordinary differential equations. Using some test problems (including stiff, mild stiff and non-stiff), it was found that the PEC mode was more efficient for non-stiff problems at crude and intermediate tolerances and the PECE mode for all problems at the stringent tolerance. An automatic switching strategy was developed using the results observed from the step size and order plots of all the test problems for both the modes and gave the optimum results. (author)

KRYSI, Ordinary Differential Equations Solver with Sdirk Krylov Method

International Nuclear Information System (INIS)

Hindmarsh, A.C.; Norsett, S.P.

2001-01-01

1 - Description of program or function: KRYSI is a set of FORTRAN subroutines for solving ordinary differential equations initial value problems. It is suitable for both stiff and non-stiff systems. When solving the implicit stage equations in the stiff case, KRYSI uses a Krylov subspace iteration method called the SPIGMR (Scaled Preconditioned Incomplete Generalized Minimum Residual) method. No explicit Jacobian storage is required, except where used in pre- conditioning. A demonstration problem is included with a description of two pre-conditioners that are natural for its solution by KRYSI. 2 - Method of solution: KRYSI uses a three-stage, third-order singly diagonally implicit Runge-Kutta (SDIRK) method. In the stiff case, a preconditioned Krylov subspace iteration within a (so-called) inexact Newton iteration is used to solve the system of nonlinear algebraic equations

Solving Partial Differential Equations Using a New Differential Evolution Algorithm

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Natee Panagant

2014-01-01

Full Text Available This paper proposes an alternative meshless approach to solve partial differential equations (PDEs. With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.

Solving polynomial differential equations by transforming them to linear functional-differential equations

OpenAIRE

Nahay, John Michael

2008-01-01

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

Substrate stiffness and oxygen as regulators of stem cell differentiation during skeletal tissue regeneration: a mechanobiological model.

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Darren Paul Burke

Full Text Available Extrinsic mechanical signals have been implicated as key regulators of mesenchymal stem cell (MSC differentiation. It has been possible to test different hypotheses for mechano-regulated MSC differentiation by attempting to simulate regenerative events such as bone fracture repair, where repeatable spatial and temporal patterns of tissue differentiation occur. More recently, in vitro studies have identified other environmental cues such as substrate stiffness and oxygen tension as key regulators of MSC differentiation; however it remains unclear if and how such cues determine stem cell fate in vivo. As part of this study, a computational model was developed to test the hypothesis that substrate stiffness and oxygen tension regulate stem cell differentiation during fracture healing. Rather than assuming mechanical signals act directly on stem cells to determine their differentiation pathway, it is postulated that they act indirectly to regulate angiogenesis and hence partially determine the local oxygen environment within a regenerating tissue. Chondrogenesis of MSCs was hypothesized to occur in low oxygen regions, while in well vascularised regions of the regenerating tissue a soft local substrate was hypothesised to facilitate adipogenesis while a stiff substrate facilitated osteogenesis. Predictions from the model were compared to both experimental data and to predictions of a well established computational mechanobiological model where tissue differentiation is assumed to be regulated directly by the local mechanical environment. The model predicted all the major events of fracture repair, including cartilaginous bridging, endosteal and periosteal bony bridging and bone remodelling. It therefore provides support for the hypothesis that substrate stiffness and oxygen play a key role in regulating MSC fate during regenerative events such as fracture healing.

Differentiation between non-neural and neural contributors to ankle joint stiffness in cerebral palsy.

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de Gooijer-van de Groep, Karin L; de Vlugt, Erwin; de Groot, Jurriaan H; van der Heijden-Maessen, Hélène C M; Wielheesen, Dennis H M; van Wijlen-Hempel, Rietje M S; Arendzen, J Hans; Meskers, Carel G M

2013-07-23

Spastic paresis in cerebral palsy (CP) is characterized by increased joint stiffness that may be of neural origin, i.e. improper muscle activation caused by e.g. hyperreflexia or non-neural origin, i.e. altered tissue viscoelastic properties (clinically: "spasticity" vs. "contracture"). Differentiation between these components is hard to achieve by common manual tests. We applied an assessment instrument to obtain quantitative measures of neural and non-neural contributions to ankle joint stiffness in CP. Twenty-three adolescents with CP and eleven healthy subjects were seated with their foot fixated to an electrically powered single axis footplate. Passive ramp-and-hold rotations were applied over full ankle range of motion (RoM) at low and high velocities. Subject specific tissue stiffness, viscosity and reflexive torque were estimated from ankle angle, torque and triceps surae EMG activity using a neuromuscular model. In CP, triceps surae reflexive torque was on average 5.7 times larger (p = .002) and tissue stiffness 2.1 times larger (p = .018) compared to controls. High tissue stiffness was associated with reduced RoM (p therapy.

Formulae of differentiation for solving differential equations with complex-valued random coefficients

International Nuclear Information System (INIS)

Kim, Ki Hong; Lee, Dong Hun

1999-01-01

Generalizing the work of Shapiro and Loginov, we derive new formulae of differentiation useful for solving differential equations with complex-valued random coefficients. We apply the formulae to the quantum-mechanical problem of noninteracting electrons moving in a correlated random potential in one dimension

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].

Science.gov (United States)

Murase, Kenya

2015-01-01

In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

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Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

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Reza Mokhtari

2012-01-01

Full Text Available On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution , is constructed by truncating the series to terms. The convergence of , to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential-difference problems.

Modified Chebyshev Collocation Method for Solving Differential Equations

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M Ziaul Arif

2015-05-01

Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.

Solving SAT Problem Based on Hybrid Differential Evolution Algorithm

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Liu, Kunqi; Zhang, Jingmin; Liu, Gang; Kang, Lishan

Satisfiability (SAT) problem is an NP-complete problem. Based on the analysis about it, SAT problem is translated equally into an optimization problem on the minimum of objective function. A hybrid differential evolution algorithm is proposed to solve the Satisfiability problem. It makes full use of strong local search capacity of hill-climbing algorithm and strong global search capability of differential evolution algorithm, which makes up their disadvantages, improves the efficiency of algorithm and avoids the stagnation phenomenon. The experiment results show that the hybrid algorithm is efficient in solving SAT problem.

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

Science.gov (United States)

Murase, Kenya

2014-01-01

Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.

Application of Monte Carlo method to solving boundary value problem of differential equations

International Nuclear Information System (INIS)

Zuo Yinghong; Wang Jianguo

2012-01-01

This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)

LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration and Root-finding

International Nuclear Information System (INIS)

Hindmarsh, A.D.; Brown, P.N.

1996-01-01

1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user. 3 - Restrictions on the complexity of the problem: None

Adams Predictor-Corrector Systems for Solving Fuzzy Differential Equations

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Dequan Shang

2013-01-01

Full Text Available A predictor-corrector algorithm and an improved predictor-corrector (IPC algorithm based on Adams method are proposed to solve first-order differential equations with fuzzy initial condition. These algorithms are generated by updating the Adams predictor-corrector method and their convergence is also analyzed. Finally, the proposed methods are illustrated by solving an example.

Solving differential–algebraic equation systems by means of index reduction methodology

DEFF Research Database (Denmark)

Sørensen, Kim; Houbak, Niels; Condra, Thomas

2006-01-01

of a number of differential equations and algebraic equations — a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODEs and index 1 DAEs by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of ordinary differential equations — ODEs....

Stiffness analysis for the micromagnetic standard problem No. 4

International Nuclear Information System (INIS)

Tsiantos, Vassilios D.; Suess, Dieter; Schrefl, Thomas; Fidler, Josef

2001-01-01

In this article solutions to micromagnetic standard problem No. 4, a 500-nmx125-nm-wide NiFe film, are presented. A three-dimensional-finite element simulation based on the solution of the Gilbert equation has been used. The simulations show that two different reversal mechanisms occur for the two different applied fields. For a field at 170 degree counterclockwise from the saturation direction there is a nonuniform rotation of magnetization towards the direction of the applied field, with the magnetization at the ends rotating faster than the magnetization in the center. For a field at 190 degree counterclockwise from the saturation direction the magnetization at the ends and in the center rotate in opposite directions leading to the formation of a 360 degree wall after 0.22 ns associated with a peak in the exchange energy. Moreover, the time for the magnetization component parallel to the long axis to cross the zero is 0.136 and 0.135 ns for field 1 and field 2, respectively. The stiffness of the problem has been investigated solving the system of ordinary differential equations with a nonstiff method (Adams) and a stiff one (backward differentiation formula, BDF). For the measure of stiffness the ratio of the total number of time steps (nst) taken by the two solvers, that is nst(Adams)/nst(BDF), has been used. This ratio is 0.784 for field 1 and 0.593 for field 2, which means that the nonstiff method (Adams) uses larger time steps than the stiff method (BDF) and consequently the systems are not stiff. The average time step for the Adams method was 0.2 ps for both fields. [copyright] 2001 American Institute of Physics

ODEPACK, Initial Value Problems of Ordinary Differential Equation System

International Nuclear Information System (INIS)

Hindmarsh, A.C.; Petzold, L.R.

2005-01-01

I - Description of program or function: ODEPACK is a collection of Fortran solvers for the initial value problem for ordinary differential equation systems. It consists of nine solvers, namely a basic solver called LSODE and eight variants of it -- LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS. The collection is suitable for both stiff and non-stiff systems. It includes solvers for systems given in explicit form, dy/dt = f(t,y), and also solvers for systems given in linearly implicit form, A(t,y) dy/dt = g(t,y). Two of the solvers use general sparse matrix solvers for the linear systems that arise. Two others use iterative (preconditioned Krylov) methods instead of direct methods for these linear systems. The most recent addition is LSODIS, which solves implicit problems with general sparse treatment of all matrices involved. The ODEPACK solvers are written in standard Fortran 77, with a few exceptions, and with minimal machine dependencies. There are separate double and single precision versions of ODEPACK. The actual solver names are those given above with a prefix of D- or S- for the double or single precision version, respectively, i.e. DLSODE/SLSODE, etc. Each solver consists of a main driver subroutine having the same name as the solver and some number of subordinate routines. For each solver, there is also a demonstration program, which solves one or two simple problems in a somewhat self-checking manner. A. Solvers for explicitly given systems. For each of the following solvers, it is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. 1. LSODE (Livermore Solver for Ordinary Differential Equations) is the basic solver of the collection. It solves stiff and non-stiff systems of the form dy/dt = f. In the stiff case, it treats the Jacobian matrix df/dy as either a dense (full) or a banded matrix, and as

Approximate analytical methods for solving ordinary differential equations

CERN Document Server

Radhika, TSL; Rani, T Raja

2015-01-01

Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete descripti

Stability of generalized Runge-Kutta methods for stiff kinetics coupled differential equations

International Nuclear Information System (INIS)

Aboanber, A E

2006-01-01

A stability and efficiency improved class of generalized Runge-Kutta methods of order 4 are developed for the numerical solution of stiff system kinetics equations for linear and/or nonlinear coupled differential equations. The determination of the coefficients required by the method is precisely obtained from the so-called equations of condition which in turn are derived by an approach based on Butcher series. Since the equations of condition are fewer in number, free parameters can be chosen for optimizing any desired feature of the process. A further related coefficient set with different values of these parameters and the region of absolute stability of the method have been introduced. In addition, the A(α) stability properties of the method are investigated. Implementing the method in a personal computer estimated the accuracy and speed of calculations and verified the good performances of the proposed new schemes for several sample problems of the stiff system point kinetics equations with reactivity feedback

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

Science.gov (United States)

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

Science.gov (United States)

Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

2013-01-01

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

Using Computer Symbolic Algebra to Solve Differential Equations.

Science.gov (United States)

Mathews, John H.

1989-01-01

This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)

Lagrange-Noether method for solving second-order differential equations

Institute of Scientific and Technical Information of China (English)

Wu Hui-Bin; Wu Run-Heng

2009-01-01

The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.

Human mesenchymal stem cells cultured on silk hydrogels with variable stiffness and growth factor differentiate into mature smooth muscle cell phenotype.

Science.gov (United States)

Floren, Michael; Bonani, Walter; Dharmarajan, Anirudh; Motta, Antonella; Migliaresi, Claudio; Tan, Wei

2016-02-01

Cell-matrix and cell-biomolecule interactions play critical roles in a diversity of biological events including cell adhesion, growth, differentiation, and apoptosis. Evidence suggests that a concise crosstalk of these environmental factors may be required to direct stem cell differentiation toward matured cell type and function. However, the culmination of these complex interactions to direct stem cells into highly specific phenotypes in vitro is still widely unknown, particularly in the context of implantable biomaterials. In this study, we utilized tunable hydrogels based on a simple high pressure CO2 method and silk fibroin (SF) the structural protein of Bombyx mori silk fibers. Modification of SF protein starting water solution concentration results in hydrogels of variable stiffness while retaining key structural parameters such as matrix pore size and β-sheet crystallinity. To further resolve the complex crosstalk of chemical signals with matrix properties, we chose to investigate the role of 3D hydrogel stiffness and transforming growth factor (TGF-β1), with the aim of correlating the effects on the vascular commitment of human mesenchymal stem cells. Our data revealed the potential to upregulate matured vascular smooth muscle cell phenotype (myosin heavy chain expression) of hMSCs by employing appropriate matrix stiffness and growth factor (within 72h). Overall, our observations suggest that chemical and physical stimuli within the cellular microenvironment are tightly coupled systems involved in the fate decisions of hMSCs. The production of tunable scaffold materials that are biocompatible and further specialized to mimic tissue-specific niche environments will be of considerable value to future tissue engineering platforms. This article investigates the role of silk fibroin hydrogel stiffness and transforming growth factor (TGF-β1), with the aim of correlating the effects on the vascular commitment of human mesenchymal stem cells. Specifically, we

Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

Directory of Open Access Journals (Sweden)

Veyis Turut

2013-01-01

Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

On Solving the Lorenz System by Differential Transformation Method

International Nuclear Information System (INIS)

Al-Sawalha, M. Mossa; Noorani, M. S. M.

2008-01-01

The differential transformation method (DTM) is employed to solve a nonlinear differential equation, namely the Lorenz system. Numerical results are compared to those obtained by the Runge–Kutta method to illustrate the preciseness and effectiveness of the proposed method. In particular, we examine the accuracy of the (DTM) as the Lorenz system changes from a non-chaotic system to a chaotic one. It is shown that the (DTM) is robust, accurate and easy to apply

Differential fracture healing resulting from fixation stiffness variability. A mouse model

International Nuclear Information System (INIS)

Gardner, M.J.; Putnam, S.M.; Wong, A.; Streubel, P.N.; Kotiya, A.; Silva, M.J.

2011-01-01

The mechanisms underlying the interaction between the local mechanical environment and fracture healing are not known. We developed a mouse femoral fracture model with implants of different stiffness, and hypothesized that differential fracture healing would result. Femoral shaft fractures were created in 70 mice, and were treated with an intramedullary nail made of either tungsten (Young's modulus=410 GPa) or aluminium (Young's modulus=70 GPa). Mice were then sacrificed at 2 or 5 weeks. Fracture calluses were analyzed using standard microCT, histological, and biomechanical methods. At 2 weeks, callus volume was significantly greater in the aluminium group than in the tungsten group (61.2 vs. 40.5 mm 3 , p=0.016), yet bone volume within the calluses was no different between the groups (13.2 vs. 12.3 mm 3 ). Calluses from the tungsten group were stiffer on mechanical testing (18.7 vs. 9.7 N/mm, p=0.01). The percent cartilage in the callus was 31.6% in the aluminium group and 22.9% in the tungsten group (p=0.40). At 5 weeks, there were no differences between any of the healed femora. In this study, fracture implants of different stiffness led to different fracture healing in this mouse fracture model. Fractures treated with a stiffer implant had more advanced healing at 2 weeks, but still healed by callus formation. Although this concept has been well documented previously, this particular model could be a valuable research tool to study the healing consequences of altered fixation stiffness, which may provide insight into the pathogenesis and ideal treatment of fractures and non-unions. (author)

Numerical solution of stiff burnup equation with short half lived nuclides by the Krylov subspace method

International Nuclear Information System (INIS)

Yamamoto, Akio; Tatsumi, Masahiro; Sugimura, Naoki

2007-01-01

The Krylov subspace method is applied to solve nuclide burnup equations used for lattice physics calculations. The Krylov method is an efficient approach for solving ordinary differential equations with stiff nature such as the nuclide burnup with short lived nuclides. Some mathematical fundamentals of the Krylov subspace method and its application to burnup equations are discussed. Verification calculations are carried out in a PWR pin-cell geometry with UO 2 fuel. A detailed burnup chain that includes 193 fission products and 28 heavy nuclides is used in the verification calculations. Shortest half life found in the present burnup chain is approximately 30 s ( 106 Rh). Therefore, conventional methods (e.g., the Taylor series expansion with scaling and squaring) tend to require longer computation time due to numerical stiffness. Comparison with other numerical methods (e.g., the 4-th order Runge-Kutta-Gill) reveals that the Krylov subspace method can provide accurate solution for a detailed burnup chain used in the present study with short computation time. (author)

A Rapid Aeroelasticity Optimization Method Based on the Stiffness characteristics

OpenAIRE

Yuan, Zhe; Huo, Shihui; Ren, Jianting

2018-01-01

A rapid aeroelasticity optimization method based on the stiffness characteristics was proposed in the present study. Large time expense in static aeroelasticity analysis based on traditional time domain aeroelasticity method is solved. Elastic axis location and torsional stiffness are discussed firstly. Both torsional stiffness and the distance between stiffness center and aerodynamic center have a direct impact on divergent velocity. The divergent velocity can be adjusted by changing the cor...

The behaviour of the local error in splitting methods applied to stiff problems

International Nuclear Information System (INIS)

Kozlov, Roman; Kvaernoe, Anne; Owren, Brynjulf

2004-01-01

Splitting methods are frequently used in solving stiff differential equations and it is common to split the system of equations into a stiff and a nonstiff part. The classical theory for the local order of consistency is valid only for stepsizes which are smaller than what one would typically prefer to use in the integration. Error control and stepsize selection devices based on classical local order theory may lead to unstable error behaviour and inefficient stepsize sequences. Here, the behaviour of the local error in the Strang and Godunov splitting methods is explained by using two different tools, Lie series and singular perturbation theory. The two approaches provide an understanding of the phenomena from different points of view, but both are consistent with what is observed in numerical experiments

LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration with Root-finding

International Nuclear Information System (INIS)

Hindmarsh, A.C.; Petzold, L.R.

2005-01-01

1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, The nonlinear iteration method-switching differs from the method-switching in LSODA and LSODAR, but provides similar savings by using the cheaper method in the non-stiff regions of the problem. c) LSODKR includes the ability to find roots of given functions of the solution during the integration. d) LSODKR also improves on the Krylov methods in LSODPK by offering the option to save and reuse the approximate Jacobian data underlying the pre-conditioner. The LSODKR source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user

Exact Stiffness for Beams on Kerr-Type Foundation: The Virtual Force Approach

Directory of Open Access Journals (Sweden)

Suchart Limkatanyu

2013-01-01

Full Text Available This paper alternatively derives the exact element stiffness equation for a beam on Kerr-type foundation. The shear coupling between the individual Winkler-spring components and the peripheral discontinuity at the boundaries between the loaded and the unloaded soil surfaces are taken into account in this proposed model. The element flexibility matrix is derived based on the virtual force principle and forms the core of the exact element stiffness matrix. The sixth-order governing differential compatibility of the problem is revealed using the virtual force principle and solved analytically to obtain the exact force interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix based on the exact force interpolation functions. The so-called “natural” element stiffness matrix is obtained by inverting the exact element flexibility matrix. One numerical example is utilized to confirm the accuracy and the efficiency of the proposed beam element on Kerr-type foundation and to show a more realistic distribution of interactive foundation force.

A neuro approach to solve fuzzy Riccati differential equations

Energy Technology Data Exchange (ETDEWEB)

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)

2015-10-22

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

A method for exponential propagation of large systems of stiff nonlinear differential equations

Science.gov (United States)

Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

1989-01-01

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Ball Bearing Stiffnesses- A New Approach Offering Analytical Expressions

Science.gov (United States)

Guay, Pascal; Frikha, Ahmed

2015-09-01

Space mechanisms use preloaded ball bearings in order to withstand the severe vibrations during launch.The launch strength requires the calculation of the bearing stiffness, but this calculation is complex. Nowadays, there is no analytical expression that gives the stiffness of a bearing. Stiffness is computed using an iterative algorithm such as Newton-Raphson, to solve the nonlinear system of equations.This paper aims at offering a simplified analytical approach, based on the assumption that the contact angle is constant. This approach gives analytical formulas of the stiffness of preloaded ball bearing.

Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

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S. Narayanamoorthy

2015-01-01

Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

International Nuclear Information System (INIS)

Mokhtari, R.; Toodar, A. Samadi; Chegini, N.G.

2011-01-01

The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with the exact solutions. The method can compete against the methods applied in the literature. (general)

Application of differential transformation method for solving dengue transmission mathematical model

Science.gov (United States)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

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Mountassir Hamdi Cherif

2017-11-01

Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

Stiffness and the automatic selection of ODE codes

International Nuclear Information System (INIS)

Shampine, L.F.

1984-01-01

The author describes the basic ideas behind the most popular methods for the numerical solution of ordinary differential equations (ODEs). He takes up the qualitative behavior of solutions of ODEs and its relation ot the propagation of numerical error. Codes for ODEs are intended either for stiff problems or for non-stiff problems. The difference is explained. Users of codes do not have the information needed to recognize stiffness. A code, DEASY, which automatically recognizes stiffness and selects a suitable method is described

Factors Affecting Differential Equation Problem Solving Ability of Students at Pre-University Level: A Conceptual Model

Science.gov (United States)

Aisha, Bibi; Zamri, Sharifa NorulAkmar Syed; Abdallah, Nabeel; Abedalaziz, Mohammad; Ahmad, Mushtaq; Satti, Umbreen

2017-01-01

In this study, different factors affecting students' differential equations (DEs) solving abilities were explored at pre university level. To explore main factors affecting students' differential equations problem solving ability, articles for a 19-year period, from 1996 to 2015, were critically reviewed and analyzed. It was revealed that…

An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

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M. Bishehniasar

2017-01-01

Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.

Stiffness Evaluation of High Temperature Superconductor Bearing Stiffness for 10 kWh Superconductor Flywheel Energy Storage System

International Nuclear Information System (INIS)

Park, B. J.; Jung, S. Y.; Lee, J. P.; Park, B. C.; Kim, C. H.; Han, S. C.; Du, S. G.; Han, Y. H.; Sung, T. H.

2009-01-01

A superconductor flywheel energy storage(SFES) system is mainly act an electro-mechanical battery which transfers mechanical energy into electrical form and vice versa. SFES system consists of a pair of non-contacting High Temperature Superconductor (HTS) bearings with a very low frictional loss. But it is essential to design an efficient HTS bearing considering with rotor dynamic properties through correct calculation of stiffness in order to support a huge composite flywheel rotor with high energy storage density. Static properties of HTS bearings provide data to solve problems which may occur easily in a running system. Since stiffness to counter vibration is the main parameter in designing an HTS bearing system, we investigate HTS bearing magnetic force through static properties between the Permanent Magnet(PM) and HTS. We measured axial / radial stiffness and found bearing stiffness can be easily changed by activated vibration direction between PM and HTS bulk. These results are used to determine the optimal design for a 10 kWh SFES.

Quasi-stationary mechanics of elastic continua with bending stiffness wrapping on a pulley system

Science.gov (United States)

Kaczmarczyk, S.; Mirhadizadeh, S.

2016-05-01

In many engineering applications elastic continua such as ropes and belts often are subject to bending when they pass over pulleys / sheaves. In this paper the quasi-stationary mechanics of a cable-pulley system is studied. The cable is modelled as a moving Euler- Bernoulli beam. The distribution of tension is non-uniform along its span and due to the bending stiffness the contact points at the pulley-beam boundaries are not unknown. The system is described by a set of nonlinear ordinary differential equations with undetermined boundary conditions. The resulting nonlinear Boundary Value Problem (BVP) with unknown boundaries is solved by converting the problem into the ‘standard’ form defined over a fixed interval. Numerical results obtained for a range of typical configurations with relevant boundary conditions applied demonstrate that due to the effects of bending stiffness the angels of wrap are reduced and the span tensions are increased.

A Simple Derivation of Kepler's Laws without Solving Differential Equations

Science.gov (United States)

Provost, J.-P.; Bracco, C.

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

On method of solving third-order ordinary differential equations directly using Bernstein polynomials

Science.gov (United States)

Khataybeh, S. N.; Hashim, I.

2018-04-01

In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

Science.gov (United States)

Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

2013-06-01

In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

Influence of Shaft Torsional Stiffness on Dynamic Response of Four-Stage Main Transmission System

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Yuan Chen

2018-01-01

Full Text Available Dynamic response analysis has potential for increasing fatigue life of the components in the transmission of a multistage main transmission system. The calculated data can demonstrate the influence of shaft torsional stiffness on dynamic characteristics of the system. Detecting key shafts of the system and analyzing their sensitivity are important for the design of four-stage helicopter gear box. Lumped mass method is applied for dynamic modeling and Fourier method is used to solve differential equation of the system. Results of the analysis indicate that key shafts can be designed carefully to improve the performance of the transmission system.

A pertinent approach to solve nonlinear fuzzy integro-differential equations.

Science.gov (United States)

Narayanamoorthy, S; Sathiyapriya, S P

2016-01-01

Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

Solving Second-Order Ordinary Differential Equations without Using Complex Numbers

Science.gov (United States)

Kougias, Ioannis E.

2009-01-01

Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…

Operator overloading as an enabling technology for automatic differentiation

International Nuclear Information System (INIS)

Corliss, G.F.; Griewank, A.

1993-01-01

We present an example of the science that is enabled by object-oriented programming techniques. Scientific computation often needs derivatives for solving nonlinear systems such as those arising in many PDE algorithms, optimization, parameter identification, stiff ordinary differential equations, or sensitivity analysis. Automatic differentiation computes derivatives accurately and efficiently by applying the chain rule to each arithmetic operation or elementary function. Operator overloading enables the techniques of either the forward or the reverse mode of automatic differentiation to be applied to real-world scientific problems. We illustrate automatic differentiation with an example drawn from a model of unsaturated flow in a porous medium. The problem arises from planning for the long-term storage of radioactive waste

Solving Differential Equations Analytically. Elementary Differential Equations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 335.

Science.gov (United States)

Goldston, J. W.

This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…

Flux weighted method for solution of stiff neutron dynamic equations and its application

International Nuclear Information System (INIS)

Li Huiyun; Jiao Huixian

1987-12-01

To analyze reactivity event for nuclear power plants, it is necessary to solve the neutron dynamic equations, which is a group of typical stiff constant differential equations. Very small time steps could only be adopted when the group of equations is solved by common methods. However, a large time steps might be selected if the Flux Weighted Medthod introduced in this paper is used. Generally, weighted factor θ i1 is set as a constant. Naturally, this treatment method can decrease the accuracy of calculation for the increase of the steadiness of solving the equations. An accurate theoretical formula of 4 x 4 matrix of θ i1 is rigorously derived so that the accuracy of calculation is ensured, as well as the steadiness of solved equations is increased. This method have the advantage over classical Runge-kutta Method and other methods. The time steps could be increased by a factor of 1 ∼ 3 orders of magnitude so as to save a lot of computating time. The programe solving neutron dynamic equation, which is prepared by using Flux Weighted Method, could be sued for real time analog of training simulator, as well as for analysis and computation of reactivity event (including rod jumping out event)

Efficient reanalysis of structures by a direct modification method. [local stiffness modifications of large structures

Science.gov (United States)

Raibstein, A. I.; Kalev, I.; Pipano, A.

1976-01-01

A procedure for the local stiffness modifications of large structures is described. It enables structural modifications without an a priori definition of the changes in the original structure and without loss of efficiency due to multiple loading conditions. The solution procedure, implemented in NASTRAN, involved the decomposed stiffness matrix and the displacement vectors of the original structure. It solves the modified structure exactly, irrespective of the magnitude of the stiffness changes. In order to investigate the efficiency of the present procedure and to test its applicability within a design environment, several real and large structures were solved. The results of the efficiency studies indicate that the break-even point of the procedure varies between 8% and 60% stiffness modifications, depending upon the structure's characteristics and the options employed.

A Variable Stiffness Analysis Model for Large Complex Thin-Walled Guide Rail

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Wang Xiaolong

2016-01-01

Full Text Available Large complex thin-walled guide rail has complicated structure and no uniform low rigidity. The traditional cutting simulations are time consuming due to huge computation especially in large workpiece. To solve these problems, a more efficient variable stiffness analysis model has been propose, which can obtain quantitative stiffness value of the machining surface. Applying simulate cutting force in sampling points using finite element analysis software ABAQUS, the single direction variable stiffness rule can be obtained. The variable stiffness matrix has been propose by analyzing multi-directions coupling variable stiffness rule. Combining with the three direction cutting force value, the reasonability of existing processing parameters can be verified and the optimized cutting parameters can be designed.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

Science.gov (United States)

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

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Sufia Zulfa Ahmad

2016-01-01

Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

Solving inverse problems for biological models using the collage method for differential equations.

Science.gov (United States)

Capasso, V; Kunze, H E; La Torre, D; Vrscay, E R

2013-07-01

In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.

An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

Directory of Open Access Journals (Sweden)

A. H. Bhrawy

2014-01-01

Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

Free Vibration Analysis for Shells of Revolution Using an Exact Dynamic Stiffness Method

Directory of Open Access Journals (Sweden)

Xudong Chen

2016-01-01

Full Text Available An exact generalised formulation for the free vibration of shells of revolution with general shaped meridians and arbitrary boundary conditions is introduced. Starting from the basic shell theories, the vibration governing equations are obtained in the Hamilton form, from which dynamic stiffness is computed using the ordinary differential equations solver COLSYS. Natural frequencies and modes are determined by employing the Wittrick-Williams (W-W algorithm in conjunction with the recursive Newton’s method, thus expanding the applications of the abovementioned techniques from one-dimensional skeletal structures to two-dimensional shells of revolution. A solution for solving the number of clamped-end frequencies J0 in the W-W algorithm is presented for both uniform and nonuniform shell segment members. Based on these theories, a FORTRAN program is written. Numerical examples on circular cylindrical shells, hyperboloidal cooling tower shells, and spherical shells are given, and error analysis is performed. The convergence of the proposed method on J0 is verified, and comparisons with frequencies from existing literature show that the dynamic stiffness method is robust, reliable, and accurate.

Systematic profiling of spatiotemporal tissue and cellular stiffness in the developing brain.

Science.gov (United States)

Iwashita, Misato; Kataoka, Noriyuki; Toida, Kazunori; Kosodo, Yoichi

2014-10-01

Accumulating evidence implicates the significance of the physical properties of the niche in influencing the behavior, growth and differentiation of stem cells. Among the physical properties, extracellular stiffness has been shown to have direct effects on fate determination in several cell types in vitro. However, little evidence exists concerning whether shifts in stiffness occur in vivo during tissue development. To address this question, we present a systematic strategy to evaluate the shift in stiffness in a developing tissue using the mouse embryonic cerebral cortex as an experimental model. We combined atomic force microscopy measurements of tissue and cellular stiffness with immunostaining of specific markers of neural differentiation to correlate the value of stiffness with the characteristic features of tissues and cells in the developing brain. We found that the stiffness of the ventricular and subventricular zones increases gradually during development. Furthermore, a peak in tissue stiffness appeared in the intermediate zone at E16.5. The stiffness of the cortical plate showed an initial increase but decreased at E18.5, although the cellular stiffness of neurons monotonically increased in association with the maturation of the microtubule cytoskeleton. These results indicate that tissue stiffness cannot be solely determined by the stiffness of the cells that constitute the tissue. Taken together, our method profiles the stiffness of living tissue and cells with defined characteristics and can therefore be utilized to further understand the role of stiffness as a physical factor that determines cell fate during the formation of the cerebral cortex and other tissues. © 2014. Published by The Company of Biologists Ltd.

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

CERN Document Server

Shingareva, Inna K

2011-01-01

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an

A novel method to solve functional differential equations

International Nuclear Information System (INIS)

Tapia, V.

1990-01-01

A method to solve differential equations containing the variational operator as the derivation operation is presented. They are called variational differential equations (VDE). The solution to a VDE should be a function containing the derivatives, with respect to the base space coordinates, of the fields up to a generic order s: a s-th-order function. The variational operator doubles the order of the function on which it acts. Therefore, in order to make compatible the orders of the different terms appearing in a VDE, the solution should be a function containing the derivatives of the fields at all orders. But this takes us again back to the functional methods. In order to avoid this, one must restrict the considerations, in the case of second-order VDEs, to the space of s-th-order functions on which the variational operator acts transitively. These functions have been characterized for a one-dimensional base space for the first- and second-order cases. These functions turn out to be polynomial in the highest-order derivatives of the fields with functions of the lower-order derivatives as coefficients. Then VDEs reduce to a system of coupled partial differential equations for the coefficients above mentioned. The importance of the method lies on the fact that the solutions to VDEs are in a one-to-one correspondence with the solutions of functional differential equations. The previous method finds direct applications in quantum field theory, where the Schroedinger equation plays a central role. Since the Schroedinger equation is reduced to a system of coupled partial differential equations, this provides a nonperturbative scheme for quantum field theory. As an example, the massless scalar field is considered

Operator-Based Preconditioning of Stiff Hyperbolic Systems

International Nuclear Information System (INIS)

Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S.

2009-01-01

We introduce an operator-based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of partial differential equations posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a characteristic decomposition of the resulting directional parts. This approach allows for solution to any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydro- dynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly-evolving dynamics, scales well to large problem sizes and numbers of processors, and allows for additional customization based on the specific problems under study

Improving Teaching Quality and Problem Solving Ability through Contextual Teaching and Learning in Differential Equations: A Lesson Study Approach

Science.gov (United States)

Khotimah, Rita Pramujiyanti; Masduki

2016-01-01

Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…

Molecular Cues Guiding Matrix Stiffness in Liver Fibrosis

Directory of Open Access Journals (Sweden)

Takaoki Saneyasu

2016-01-01

Full Text Available Tissue and matrix stiffness affect cell properties during morphogenesis, cell growth, differentiation, and migration and are altered in the tissue remodeling following injury and the pathological progression. However, detailed molecular mechanisms underlying alterations of stiffness in vivo are still poorly understood. Recent engineering technologies have developed powerful techniques to characterize the mechanical properties of cell and matrix at nanoscale levels. Extracellular matrix (ECM influences mechanical tension and activation of pathogenic signaling during the development of chronic fibrotic diseases. In this short review, we will focus on the present knowledge of the mechanisms of how ECM stiffness is regulated during the development of liver fibrosis and the molecules involved in ECM stiffness as a potential therapeutic target for liver fibrosis.

Inverse axial mounting stiffness design for lithographic projection lenses.

Science.gov (United States)

Wen-quan, Yuan; Hong-bo, Shang; Wei, Zhang

2014-09-01

In order to balance axial mounting stiffness of lithographic projection lenses and the image quality under dynamic working conditions, an easy inverse axial mounting stiffness design method is developed in this article. Imaging quality deterioration at the wafer under different axial vibration levels is analyzed. The desired image quality can be determined according to practical requirements, and axial vibrational tolerance of each lens is solved with the damped least-squares method. Based on adaptive interval adjustment, a binary search algorithm, and the finite element method, the axial mounting stiffness of each lens can be traveled in a large interval, and converges to a moderate numerical solution which makes the axial vibrational amplitude of the lens converge to its axial vibrational tolerance. Model simulation is carried out to validate the effectiveness of the method.

Who Solved the Bernoulli Differential Equation and How Did They Do It?

Science.gov (United States)

Parker, Adam E.

2013-01-01

The Bernoulli brothers, Jacob and Johann, and Leibniz: Any of these might have been first to solve what is called the Bernoulli differential equation. We explore their ideas and the chronology of their work, finding out, among other things, that variation of parameters was used in 1697, 78 years before 1775, when Lagrange introduced it in general.

A MATLAB Script for Solving 2D/3D Minimum Compliance Problems using Anisotropic Mesh Adaptation

DEFF Research Database (Denmark)

Jensen, Kristian Ejlebjerg

2017-01-01

We present a pure MATLAB implementation for solving 2D/3D compliance minimization problems using the density method. A filtered design variable with a minimum length is computed using a Helmholtz-type differential equation. The optimality criteria is used as optimizer and to avoid local minima we...... apply continuation of an exponent that controls the stiffness associated with intermediate design variables. We constrain the volume from above and use the implementation to show that optimizations with dynamic meshes can save significant amounts of computational time compared to fixed meshes without...

Solving ordinary differential equations by electrical analogy: a multidisciplinary teaching tool

Science.gov (United States)

Sanchez Perez, J. F.; Conesa, M.; Alhama, I.

2016-11-01

Ordinary differential equations are the mathematical formulation for a great variety of problems in science and engineering, and frequently, two different problems are equivalent from a mathematical point of view when they are formulated by the same equations. Students acquire the knowledge of how to solve these equations (at least some types of them) using protocols and strict algorithms of mathematical calculation without thinking about the meaning of the equation. The aim of this work is that students learn to design network models or circuits in this way; with simple knowledge of them, students can establish the association of electric circuits and differential equations and their equivalences, from a formal point of view, that allows them to associate knowledge of two disciplines and promote the use of this interdisciplinary approach to address complex problems. Therefore, they learn to use a multidisciplinary tool that allows them to solve these kinds of equations, even students of first course of engineering, whatever the order, grade or type of non-linearity. This methodology has been implemented in numerous final degree projects in engineering and science, e.g., chemical engineering, building engineering, industrial engineering, mechanical engineering, architecture, etc. Applications are presented to illustrate the subject of this manuscript.

A comparative study on free vibration analysis of delaminated torsion stiff and bending stiff composite shells

International Nuclear Information System (INIS)

Dey, Sudip; Karmakar, Amit

2013-01-01

This paper presents a finite element method to compare the effects of delamination on free vibration of graphite-epoxy bending stiff and torsion stiff composite pretwisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting the Coriolis effect for moderate rotational speeds. An eight noded isoparametric plate bending element is employed incorporating rotary inertia and effects of transverse shear deformation based on Mindlin's theory. The multipoint constraint; algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Mode shapes for typical configurations are also depicted. Numerical results obtained are the first known non-dimensional frequencies which could serve as reference solutions for the future investigators.

3D Scaffolds with Different Stiffness but the Same Microstructure for Bone Tissue Engineering.

Science.gov (United States)

Chen, Guobao; Dong, Chanjuan; Yang, Li; Lv, Yonggang

2015-07-29

A growing body of evidence has shown that extracellular matrix (ECM) stiffness can modulate stem cell adhesion, proliferation, migration, differentiation, and signaling. Stem cells can feel and respond sensitively to the mechanical microenvironment of the ECM. However, most studies have focused on classical two-dimensional (2D) or quasi-three-dimensional environments, which cannot represent the real situation in vivo. Furthermore, most of the current methods used to generate different mechanical properties invariably change the fundamental structural properties of the scaffolds (such as morphology, porosity, pore size, and pore interconnectivity). In this study, we have developed novel three-dimensional (3D) scaffolds with different degrees of stiffness but the same 3D microstructure that was maintained by using decellularized cancellous bone. Mixtures of collagen and hydroxyapatite [HA: Ca10(PO4)6(OH)2] with different proportions were coated on decellularized cancellous bone to vary the stiffness (local stiffness, 13.00 ± 5.55 kPa, 13.87 ± 1.51 kPa, and 37.7 ± 19.6 kPa; bulk stiffness, 6.74 ± 1.16 kPa, 8.82 ± 2.12 kPa, and 23.61 ± 8.06 kPa). Microcomputed tomography (μ-CT) assay proved that there was no statistically significant difference in the architecture of the scaffolds before or after coating. Cell viability, osteogenic differentiation, cell recruitment, and angiogenesis were determined to characterize the scaffolds and evaluate their biological responses in vitro and in vivo. The in vitro results indicate that the scaffolds developed in this study could sustain adhesion and growth of rat mesenchymal stem cells (MSCs) and promote their osteogenic differentiation. The in vivo results further demonstrated that these scaffolds could help to recruit MSCs from subcutaneous tissue, induce them to differentiate into osteoblasts, and provide the 3D environment for angiogenesis. These findings showed that the method we developed can build scaffolds with

Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane-Emden type differential equations (LETDEs).

Science.gov (United States)

Tripathi, Rajnee; Mishra, Hradyesh Kumar

2016-01-01

In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.

Solving differential equations for Feynman integrals by expansions near singular points

Science.gov (United States)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Neural network error correction for solving coupled ordinary differential equations

Science.gov (United States)

Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.

1992-01-01

A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.

A semi-analytical approach for solving of nonlinear systems of functional differential equations with delay

Science.gov (United States)

Rebenda, Josef; Šmarda, Zdeněk

2017-07-01

In the paper, we propose a correct and efficient semi-analytical approach to solve initial value problem for systems of functional differential equations with delay. The idea is to combine the method of steps and differential transformation method (DTM). In the latter, formulas for proportional arguments and nonlinear terms are used. An example of using this technique for a system with constant and proportional delays is presented.

Solving (2 + 1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

International Nuclear Information System (INIS)

Ka-Lin, Su; Yuan-Xi, Xie

2010-01-01

By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)

A toolbox to solve coupled systems of differential and difference equations

International Nuclear Information System (INIS)

Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de

2016-01-01

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.

A toolbox to solve coupled systems of differential and difference equations

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Schneider, Carsten [Linz Univ. (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Freitas, Abilio de [DESY Zeuthen (Germany)

2016-01-15

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.

Nuclear safety code study. Final report

International Nuclear Information System (INIS)

Jackson, C.; Abumansoor, K.; Myers, E.; Jesperson, D.; Cramer, E.; O'Reilly, B.; Carmichael, B.

1980-06-01

An unprotected overpower accident in a Liquid Metal Fast Breeder Reactor is studied. We construct a mathematical model and derive a system of partial differential equations for the temperature. After spatial discretization, we have a large system of ordinary differential equations; the system is stiff. We solve the steady state version of our equations analytically and obtain good agreement with other work. Then we solve the time-dependent problem numerically, using two stiff techniques and one non-stiff technique. The stiff techniques are vastly more efficient than the non-stiff technique. Between the two stiff techniques, the Gear backward differentiation formulas are more efficient than an implicit Runge-Kutta type method. We also compare the use of the full neutron kinetics equations to an approximation called the zero-lifetime system. Use of the zero-lifetime system is thought to make the problem easier to solve. Results indicate this is not true when a good stiff method is used. Thus use of the zero-lifetime system is probably not necessary, and should be avoided

An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

Science.gov (United States)

Alam Khan, Najeeb; Razzaq, Oyoon Abdul

2016-03-01

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

Solving differential equations with unknown constitutive relations as recurrent neural networks

Energy Technology Data Exchange (ETDEWEB)

Hagge, Tobias J.; Stinis, Panagiotis; Yeung, Enoch H.; Tartakovsky, Alexandre M.

2017-12-08

We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and use a recurrent neural network to “learn” the reaction rate from this data. This is achieved by including discretized ordinary differential equations as part of a recurrent neural network training problem. We extend TensorFlow’s recurrent neural network architecture to create a simple but scalable and effective solver for the unknown functions, and apply it to a fedbatch bioreactor simulation problem. Use of techniques from recent deep learning literature enables training of functions with behavior manifesting over thousands of time steps. Our networks are structurally similar to recurrent neural networks, but differ in purpose, and require modified training strategies.

Differential rigor development in red and white muscle revealed by simultaneous measurement of tension and stiffness.

Science.gov (United States)

Kobayashi, Masahiko; Takemori, Shigeru; Yamaguchi, Maki

2004-02-10

Based on the molecular mechanism of rigor mortis, we have proposed that stiffness (elastic modulus evaluated with tension response against minute length perturbations) can be a suitable index of post-mortem rigidity in skeletal muscle. To trace the developmental process of rigor mortis, we measured stiffness and tension in both red and white rat skeletal muscle kept in liquid paraffin at 37 and 25 degrees C. White muscle (in which type IIB fibres predominate) developed stiffness and tension significantly more slowly than red muscle, except for soleus red muscle at 25 degrees C, which showed disproportionately slow rigor development. In each of the examined muscles, stiffness and tension developed more slowly at 25 degrees C than at 37 degrees C. In each specimen, tension always reached its maximum level earlier than stiffness, and then decreased more rapidly and markedly than stiffness. These phenomena may account for the sequential progress of rigor mortis in human cadavers.

Taylor's series method for solving the nonlinear point kinetics equations

International Nuclear Information System (INIS)

Nahla, Abdallah A.

2011-01-01

Highlights: → Taylor's series method for nonlinear point kinetics equations is applied. → The general order of derivatives are derived for this system. → Stability of Taylor's series method is studied. → Taylor's series method is A-stable for negative reactivity. → Taylor's series method is an accurate computational technique. - Abstract: Taylor's series method for solving the point reactor kinetics equations with multi-group of delayed neutrons in the presence of Newtonian temperature feedback reactivity is applied and programmed by FORTRAN. This system is the couples of the stiff nonlinear ordinary differential equations. This numerical method is based on the different order derivatives of the neutron density, the precursor concentrations of i-group of delayed neutrons and the reactivity. The r th order of derivatives are derived. The stability of Taylor's series method is discussed. Three sets of applications: step, ramp and temperature feedback reactivities are computed. Taylor's series method is an accurate computational technique and stable for negative step, negative ramp and temperature feedback reactivities. This method is useful than the traditional methods for solving the nonlinear point kinetics equations.

Association of Gastrocnemius Muscle Stiffness With Passive Ankle Joint Stiffness and Sex-Related Difference in the Joint Stiffness.

Science.gov (United States)

Chino, Kintaro; Takashi, Hideyuki

2017-11-15

Passive ankle joint stiffness is affected by all structures located within and over the joint, and is greater in men than in women. Localized muscle stiffness can be assessed by ultrasound shear wave elastography, and muscle architecture such as fascicle length and pennation angle can be measured by B-mode ultrasonography. Thus, we assessed localized muscle stiffness of the medial gastrocnemius (MG) with consideration of individual variability in the muscle architecture, and examined the association of the muscle stiffness with passive ankle joint stiffness and the sex-related difference in the joint stiffness. Localized muscle stiffness of the MG in 16 men and 17 women was assessed at 10° and 20° plantar flexion, neutral anatomical position, 10° and 20° dorsiflexion. Fascicle length and pennation angle of the MG were measured at these joint positions. Passive ankle joint stiffness was determined by the ankle joint angle-torque relationship. Localized MG muscle stiffness was not significantly correlated with passive ankle joint stiffness, and did not show significant sex-related difference, even when considering the muscle architecture. This finding suggest that muscle stiffness of the MG would not be a prominent factor to determine passive ankle joint stiffness and the sex-related difference in the joint stiffness.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

Science.gov (United States)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

Science.gov (United States)

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

Advantages and Disadvantages of Using MATLAB/ode45 for Solving Differential Equations in Engineering Applications

OpenAIRE

Waleed K. Ahmed

2013-01-01

The present paper demonstrates the route used for solving differential equations for the engineering applications at UAEU. Usually students at the Engineering Requirements Unit (ERU) stage of the Faculty of Engineering at the UAEU must enroll in a course of Differential Equations and Engineering Applications (MATH 2210) as a prerequisite for the subsequent stages of their study. Mainly, one of the objectives of this course is that the students practice MATLAB software package during the cours...

Pulling a polymer with anisotropic stiffness near a sticky wall

International Nuclear Information System (INIS)

Tabbara, R; Owczarek, A L

2012-01-01

We solve exactly a two-dimensional partially directed walk model of a semi-flexible polymer that has one end tethered to a sticky wall, while a pulling force away from the adsorbing surface acts on the free end of the walk. This model generalizes a number of previously considered adsorption models by incorporating individual horizontal and vertical stiffness effects, in competition with a variable pulling angle. A solution to the corresponding generating function is found by means of the kernel method. While the phases and related phase transitions are similar in nature to those found previously the analysis of the model in terms of its physical variables highlights various novel structures in the shapes of the phase diagrams and related behaviour of the polymer. We review the results of previously considered sub-cases, augmenting these findings to include analysis with respect to the model’s physical variables—namely, temperature, pulling force, pulling angle away from the surface, stiffness strength and the ratio of vertical to horizontal stiffness potentials, with our subsequent analysis for the general model focusing on the effect that stiffness has on this pulling angle range. In analysing the model with stiffness we also pay special attention to the case where only vertical stiffness is included. The physical analysis of this case reveals behaviour more closely resembling that of an upward pulling force acting on a polymer than it does of a model where horizontal stiffness acts. The stiffness–temperature phase diagram exhibits re-entrance for low temperatures, previously only seen for three-dimensional or co-polymer models. For the most general model we delineate the shift in the physical behaviour as we change the ratio of vertical to horizontal stiffness between the horizontal-only and the vertical-only stiffness regimes. We find that a number of distinct physical characteristics will only be observed for a model where the vertical stiffness dominates

Online Identification and Verification of the Elastic Coupling Torsional Stiffness

Directory of Open Access Journals (Sweden)

Wanyou Li

2016-01-01

Full Text Available To analyze the torsional vibration of a diesel engine shaft, the torsional stiffness of the flexible coupling is a key kinetic parameter. Since the material properties of the elastic element of the coupling might change after a long-time operation due to the severe working environment or improper use and the variation of such properties will change dynamic feature of the coupling, it will cause a relative large calculation error of torsional vibration to the shaft system. Moreover, the torsional stiffness of the elastic coupling is difficult to be determined, and it is inappropriate to measure this parameter by disassembling the power unit while it is under normal operation. To solve these problems, this paper comes up with a method which combines the torsional vibration test with the calculation of the diesel shafting and uses the inherent characteristics of shaft torsional vibration to identify the dynamic stiffness of the elastic coupling without disassembling the unit. Analysis results show that it is reasonable and feasible to identify the elastic coupling dynamic torsional stiffness with this method and the identified stiffness is accurate. Besides, this method provides a convenient and practical approach to examine the dynamic behavior of the long running elastic coupling.

Increased Stiffness in Aged Skeletal Muscle Impairs Muscle Progenitor Cell Proliferative Activity.

Directory of Open Access Journals (Sweden)

Grégory Lacraz

Full Text Available Skeletal muscle aging is associated with a decreased regenerative potential due to the loss of function of endogenous stem cells or myogenic progenitor cells (MPCs. Aged skeletal muscle is characterized by the deposition of extracellular matrix (ECM, which in turn influences the biomechanical properties of myofibers by increasing their stiffness. Since the stiffness of the MPC microenvironment directly impacts MPC function, we hypothesized that the increase in muscle stiffness that occurs with aging impairs the behavior of MPCs, ultimately leading to a decrease in regenerative potential.We showed that freshly isolated individual myofibers from aged mouse muscles contain fewer MPCs overall than myofibers from adult muscles, with fewer quiescent MPCs and more proliferative and differentiating MPCs. We observed alterations in cultured MPC behavior in aged animals, where the proliferation and differentiation of MPCs were lower and higher, respectively. These alterations were not linked to the intrinsic properties of aged myofibers, as shown by the similar values for the cumulative population-doubling values and fusion indexes. However, atomic force microscopy (AFM indentation experiments revealed a nearly 4-fold increase in the stiffness of the MPC microenvironment. We further showed that the increase in stiffness is associated with alterations to muscle ECM, including the accumulation of collagen, which was correlated with higher hydroxyproline and advanced glycation end-product content. Lastly, we recapitulated the impaired MPC behavior observed in aging using a hydrogel substrate that mimics the stiffness of myofibers.These findings provide novel evidence that the low regenerative potential of aged skeletal muscle is independent of intrinsic MPC properties but is related to the increase in the stiffness of the MPC microenvironment.

VODE, Variable Coefficient Ordinary Differential Equations (ODE) Solver

International Nuclear Information System (INIS)

Brown, P.N.; Hindmarsh, A.C.; Byrne, G.D.

2002-01-01

1 - Description of program or function: VODE is a package of subroutines for the numerical solution of the initial-value problem for systems of first-order ordinary differential equations. The package can be used for either stiff or non-stiff systems. In the stiff case, the Jacobian matrix is treated as full or banded. An algorithm is included for saving and reusing the Jacobian matrix under certain conditions. If storage is limited, this option may be suppressed. 2 - Method of solution - VODE uses the variable-order, variable- coefficient Adams-Moulton method for non-stiff systems and the variable-order, fixed-leading-coefficient Backward Differentiation Formula (BDF) method for stiff systems

Solving Ordinary Differential Equations

Science.gov (United States)

Krogh, F. T.

1987-01-01

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

A stable computational scheme for stiff time-dependent constitutive equations

International Nuclear Information System (INIS)

Shih, C.F.; Delorenzi, H.G.; Miller, A.K.

1977-01-01

Viscoplasticity and creep type constitutive equations are increasingly being employed in finite element codes for evaluating the deformation of high temperature structural members. These constitutive equations frequently exhibit stiff regimes which makes an analytical assessment of the structure very costly. A computational scheme for handling deformation in stiff regimes is proposed in this paper. By the finite element discretization, the governing partial differential equations in the spatial (x) and time (t) variables are reduced to a system of nonlinear ordinary differential equations in the independent variable t. The constitutive equations are expanded in a Taylor's series about selected values of t. The resulting system of differential equations are then integrated by an implicit scheme which employs a predictor technique to initiate the Newton-Raphson procedure. To examine the stability and accuracy of the computational scheme, a series of calculations were carried out for uniaxial specimens and thick wall tubes subjected to mechanical and thermal loading. (Auth.)

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

Science.gov (United States)

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

A simple derivation of Kepler's laws without solving differential equations

International Nuclear Information System (INIS)

Provost, J-P; Bracco, C

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to an explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by undergraduates or by secondary school teachers (who might use it with their pupils), can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

Algorithms to solve coupled systems of differential equations in terms of power series

International Nuclear Information System (INIS)

Ablinger, Jakob; Schneider, Carsten

2016-08-01

Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations, and that sufficiently many initial values of the integrals are given. Then there exist algorithms that decide constructively if the coefficients of their power series representations can be given within the class of nested sums over hypergeometric products. In this article we work out the calculation steps that solve this problem. First, we present a successful tactic that has been applied recently to challenging problems coming from massive 3-loop Feynman integrals. Here our main tool is to solve scalar linear recurrences within the class of nested sums over hypergeometric products. Second, we will present a new variation of this tactic which relies on more involved summation technologies but succeeds in reducing the problem to solve scalar recurrences with lower recurrence orders. The article works out the different challenges of this new tactic and demonstrates how they can be treated efficiently with our existing summation technologies.

Independent control of matrix adhesiveness and stiffness within a 3D self-assembling peptide hydrogel.

Science.gov (United States)

Hogrebe, Nathaniel J; Reinhardt, James W; Tram, Nguyen K; Debski, Anna C; Agarwal, Gunjan; Reilly, Matthew A; Gooch, Keith J

2018-04-01

A cell's insoluble microenvironment has increasingly been shown to exert influence on its function. In particular, matrix stiffness and adhesiveness strongly impact behaviors such as cell spreading and differentiation, but materials that allow for independent control of these parameters within a fibrous, stromal-like microenvironment are very limited. In the current work, we devise a self-assembling peptide (SAP) system that facilitates user-friendly control of matrix stiffness and RGD (Arg-Gly-Asp) concentration within a hydrogel possessing a microarchitecture similar to stromal extracellular matrix. In this system, the RGD-modified SAP sequence KFE-RGD and the scrambled sequence KFE-RDG can be directly swapped for one another to change RGD concentration at a given matrix stiffness and total peptide concentration. Stiffness is controlled by altering total peptide concentration, and the unmodified base peptide KFE-8 can be included to further increase this stiffness range due to its higher modulus. With this tunable system, we demonstrate that human mesenchymal stem cell morphology and differentiation are influenced by both gel stiffness and the presence of functional cell binding sites in 3D culture. Specifically, cells 24 hours after encapsulation were only able to spread out in stiffer matrices containing KFE-RGD. Upon addition of soluble adipogenic factors, soft gels facilitated the greatest adipogenesis as determined by the presence of lipid vacuoles and PPARγ-2 expression, while increasing KFE-RGD concentration at a given stiffness had a negative effect on adipogenesis. This three-component hydrogel system thus allows for systematic investigation of matrix stiffness and RGD concentration on cell behavior within a fibrous, three-dimensional matrix. Physical cues from a cell's surrounding environment-such as the density of cell binding sites and the stiffness of the surrounding material-are increasingly being recognized as key regulators of cell function

The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

KAUST Repository

Piret, Cécile

2012-05-01

Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.

Coupling between the Output Force and Stiffness in Different Variable Stiffness Actuators

Directory of Open Access Journals (Sweden)

Amir Jafari

2014-08-01

Full Text Available The fundamental objective in developing variable stiffness actuators is to enable the actuator to deliberately tune its stiffness. This is done through controlling the energy flow extracted from internal power units, i.e., the motors of a variable stiffness actuator (VSA. However, the stiffness may also be unintentionally affected by the external environment, over which, there is no control. This paper analysis the correlation between the external loads, applied to different variable stiffness actuators, and their resultant output stiffness. Different types of variable stiffness actuators have been studied considering springs with different types of nonlinearity. The results provide some insights into how to design the actuator mechanism and nonlinearity of the springs in order to increase the decoupling between the load and stiffness in these actuators. This would significantly widen the application range of a variable stiffness actuator.

Composition Feature of the Element Tangent Stiffness Matrix of Geometrically Nonlinear 2D Frame Structures

Directory of Open Access Journals (Sweden)

Romanas Karkauskas

2011-04-01

Full Text Available The expressions of the finite element method tangent stiffness matrix of geometrically nonlinear constructions are not fully presented in publications. The matrixes of small displacements stiffness are usually presented only. To solve various problems of construction analysis or design and to specify the mode of the real deflection of construction, it is necessary to have a fully described tangent matrix analytical expression. This paper presents a technique of tangent stiffness matrix generation using discrete body total potential energy stationary conditions considering geometrically nonlinear 2D frame element taking account of interelement interaction forces only. The obtained vector-function derivative of internal forces considering nodal displacements is the tangent stiffness matrix. The analytical expressions having nodal displacements of matrixes forming the content of the 2D frame construction element tangent stiffness matrix are presented in the article. The suggested methodology has been checked making symbolical calculations in the medium of MatLAB calculation complex. The analytical expression of the stiffness matrix has been obtained.Article in Lithuanian

Efficient integration of stiff kinetics with phase change detection for reactive reservoir processes

DEFF Research Database (Denmark)

Kristensen, Morten Rode; Gerritsen, Margot G.; Thomsen, Per Grove

2007-01-01

We propose the use of implicit one-step Explicit Singly Diagonal Implicit Runge-Kutta (ESDIRK) methods for integration of the stiff kinetics in reactive, compositional and thermal processes that are solved using operator-splitting type approaches. To facilitate the algorithmic development we...

New numerical approximation for solving fractional delay differential equations of variable order using artificial neural networks

Science.gov (United States)

Zúñiga-Aguilar, C. J.; Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Martínez, V. M.; Romero-Ugalde, H. M.

2018-02-01

In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated.

Using CUDA Technology for Defining the Stiffness Matrix in the Subspace of Eigenvectors

Directory of Open Access Journals (Sweden)

Yu. V. Berchun

2015-01-01

Full Text Available The aim is to improve the performance of solving a problem of deformable solid mechanics through the use of GPGPU. The paper describes technologies for computing systems using both a central and a graphics processor and provides motivation for using CUDA technology as the efficient one.The paper also analyses methods to solve the problem of defining natural frequencies and design waveforms, i.e. an iteration method in the subspace. The method includes several stages. The paper considers the most resource-hungry stage, which defines the stiffness matrix in the subspace of eigenforms and gives the mathematical interpretation of this stage.The GPU choice as a computing device is justified. The paper presents an algorithm for calculating the stiffness matrix in the subspace of eigenforms taking into consideration the features of input data. The global stiffness matrix is very sparse, and its size can reach tens of millions. Therefore, it is represented as a set of the stiffness matrices of the single elements of a model. The paper analyses methods of data representation in the software and selects the best practices for GPU computing.It describes the software implementation using CUDA technology to calculate the stiffness matrix in the subspace of eigenforms. Due to the input data nature, it is impossible to use the universal libraries of matrix computations (cuSPARSE and cuBLAS for loading the GPU. For efficient use of GPU resources in the software implementation, the stiffness matrices of elements are built in the block matrices of a special form. The advantages of using shared memory in GPU calculations are described.The transfer to the GPU computations allowed a twentyfold increase in performance (as compared to the multithreaded CPU-implementation on the model of middle dimensions (degrees of freedom about 2 million. Such an acceleration of one stage speeds up defining the natural frequencies and waveforms by the iteration method in a subspace

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

Science.gov (United States)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

Energy Technology Data Exchange (ETDEWEB)

Moryakov, A. V., E-mail: sailor@orc.ru [National Research Centre Kurchatov Institute (Russian Federation)

2016-12-15

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials

Directory of Open Access Journals (Sweden)

Jianping Liu

2016-01-01

Full Text Available An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived based on the second kind of Chebyshev polynomials. Using two types of operational matrixes, the original equation is transformed into the arithmetic product of several dependent matrixes, which can be viewed as an algebraic system after adopting the collocation points. Further, numerical solution of original equation is obtained by solving the algebraic system. Finally, several examples show that the numerical algorithm is computationally efficient.

Matrix stiffness reverses the effect of actomyosin tension on cell proliferation.

Science.gov (United States)

Mih, Justin D; Marinkovic, Aleksandar; Liu, Fei; Sharif, Asma S; Tschumperlin, Daniel J

2012-12-15

The stiffness of the extracellular matrix exerts powerful effects on cell proliferation and differentiation, but the mechanisms transducing matrix stiffness into cellular fate decisions remain poorly understood. Two widely reported responses to matrix stiffening are increases in actomyosin contractility and cell proliferation. To delineate their relationship, we modulated cytoskeletal tension in cells grown across a physiological range of matrix stiffnesses. On both synthetic and naturally derived soft matrices, and across a panel of cell types, we observed a striking reversal of the effect of inhibiting actomyosin contractility, switching from the attenuation of proliferation on rigid substrates to the robust promotion of proliferation on soft matrices. Inhibiting contractility on soft matrices decoupled proliferation from cytoskeletal tension and focal adhesion organization, but not from cell spread area. Our results demonstrate that matrix stiffness and actomyosin contractility converge on cell spreading in an unexpected fashion to control a key aspect of cell fate.

The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

KAUST Repository

Piret, Cé cile

2012-01-01

Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper

Memory functioning and negative symptoms as differential predictors of social problem solving skills in schizophrenia.

Science.gov (United States)

Ventura, Joseph; Tom, Shelley R; Jetton, Chris; Kern, Robert S

2013-02-01

Neurocognition in general, and memory functioning in particular, as well as symptoms have all been shown to be related to social problem solving (SPS) in schizophrenia. However, few studies have directly compared the relative contribution of neurocognition vs. psychiatric symptoms to the components of SPS. Sixty outpatients (aged 21-65) who met DSM-IV criteria for schizophrenia or schizoaffective disorder were administered a broad battery of memory tests and assessed for severity of positive and negative symptoms as part of a baseline assessment of a study of psychiatric rehabilitation. Multiple regression analyses were used to examine the contribution of memory functioning vs. symptoms on receiving, processing, and sending skill areas of social problem solving ability. An index of verbal learning was the strongest predictor of processing skills whereas negative symptoms were the strongest predictor of sending skills. Positive symptoms were not related to any of the three skill areas of social problem solving. Memory functioning and psychiatric symptoms differentially predict selected areas of social problem solving ability in persons with schizophrenia. Consistent with other reports, positive symptoms were not related to social problem solving. Consideration of both neurocognition and negative symptoms may be important to the development of rehabilitation interventions in this area of functioning. Copyright © 2012 Elsevier B.V. All rights reserved.

Construction of Interval Wavelet Based on Restricted Variational Principle and Its Application for Solving Differential Equations

OpenAIRE

Mei, Shu-Li; Lv, Hong-Liang; Ma, Qin

2008-01-01

Based on restricted variational principle, a novel method for interval wavelet construction is proposed. For the excellent local property of quasi-Shannon wavelet, its interval wavelet is constructed, and then applied to solve ordinary differential equations. Parameter choices for the interval wavelet method are discussed and its numerical performance is demonstrated.

A Three Revolute-Revolute-Spherical wearable fingertip cutaneous device for stiffness rendering

DEFF Research Database (Denmark)

Chinello, Francesco; Pacchierotti, Claudio; Malvezzi, Monica

2017-01-01

the capability of our device in differentiating stiffness information, while the second one focused on evaluating its applicability in an immersive virtual reality scenario. Results showed the effectiveness of the proposed wearable solution, with a JND for stiffness of 208.5 ± 17.2 N/m. Moreover, all subjects...... preferred the virtual interaction experience when provided with wearable cutaneous feedback, even if results also showed that subjects found our device still a bit difficult to use....

OroSTIFF: Face-referenced measurement of perioral stiffness in health and disease.

Science.gov (United States)

Chu, Shin-Ying; Barlow, Steven M; Kieweg, Douglas; Lee, Jaehoon

2010-05-28

A new device and automated measurement technology known as OroSTIFF is described to characterize non-participatory perioral stiffness in healthy adults for eventual application to patients with orofacial movement disorders associated with neuromotor disease, traumatic injury, or congenital clefts of the upper lip. Previous studies of perioral biomechanics required head stabilization for extended periods of time during measurement, which precluded sampling patients with involuntary body/head movements (dyskinesias), or pediatric subjects. The OroSTIFF device is face-referenced and avoids the complications associated with head-restraint. Supporting data of non-participatory perioral tissue stiffness using OroSTIFF are included from 10 male and 10 female healthy subjects. The OroSTIFF device incorporates a pneumatic glass air cylinder actuator instrumented for pressure, and an integrated subminiature displacement sensor to encode lip aperture. Perioral electromyograms were simultaneously sampled to confirm passive muscle state for the superior and inferior divisions of the orbicularis oris muscles. Perioral stiffness, derived as a quotient from resultant force (DeltaF) and interangle span (DeltaX), was modeled with multilevel regression techniques. Real-time calculation of the perioral stiffness function demonstrated a significant quadratic relation between imposed interangle stretch and resultant force. This stiffness growth function also differed significantly between males and females. This study demonstrates the OroSTIFF 'proof-of-concept' for cost-effective non-invasive stimulus generation and derivation of perioral stiffness in a group of healthy unrestrained adults, and a case study to illustrate the dose-dependent effects of Levodopa on perioral stiffness in an individual with advanced Parkinson's disease who exhibited marked dyskinesia and rigidity. Copyright 2010 Elsevier Ltd. All rights reserved.

Kirchhoff plate theory-based electromechanically-coupled analytical model considering inertia and stiffness effects of a surface-bonded piezoelectric patch

International Nuclear Information System (INIS)

Yoon, Heonjun; Youn, Byeng D; Kim, Heung Soo

2016-01-01

As a compact and durable design concept, piezoelectric energy harvesting skin (PEH skin) has been recently proposed for self-powered electronic device applications. This study aims to develop an electromechanically-coupled analytical model of PEH skin considering the inertia and stiffness effects of a piezoelectric patch. Based on Kirchhoff plate theory, Hamilton’s principle is used to derive the electromechanically-coupled differential equation of motion. Due to the geometric discontinuity of the piezoelectric patch, the Rayleigh–Ritz method is applied to calculate the natural frequency and corresponding mode shapes. The electrical circuit equation is derived from Gauss’s law. Output voltage is estimated by solving the equation of motion and electrical circuit equation, simultaneously. For the purpose of evaluating the predictive capability, the results of the electromechanically-coupled analytical model are compared with those of the finite element method in a hierarchical manner. The outstanding merits of the electromechanically-coupled analytical model of PEH skin are three-fold: (1) consideration of the inertia and stiffness effects of the piezoelectric patches; (2) physical parameterization between the two-dimensional mechanical configuration and piezoelectric transduction; (3) manipulability of the twisting modes of a cantilever plate with a small aspect ratio. (paper)

Load bearing and stiffness tailored NiTi implants produced by additive manufacturing: a simulation study

Science.gov (United States)

Rahmanian, Rasool; Shayesteh Moghaddam, Narges; Haberland, Christoph; Dean, David; Miller, Michael; Elahinia, Mohammad

2014-03-01

Common metals for stable long-term implants (e.g. stainless steel, Titanium and Titanium alloys) are much stiffer than spongy cancellous and even stiffer than cortical bone. When bone and implant are loaded this stiffness mismatch results in stress shielding and as a consequence, degradation of surrounding bony structure can lead to disassociation of the implant. Due to its lower stiffness and high reversible deformability, which is associated with the superelastic behavior, NiTi is an attractive biomaterial for load bearing implants. However, the stiffness of austenitic Nitinol is closer to that of bone but still too high. Additive manufacturing provides, in addition to the fabrication of patient specific implants, the ability to solve the stiffness mismatch by adding engineered porosity to the implant. This in turn allows for the design of different stiffness profiles in one implant tailored to the physiological load conditions. This work covers a fundamental approach to bring this vision to reality. At first modeling of the mechanical behavior of different scaffold designs are presented as a proof of concept of stiffness tailoring. Based on these results different Nitinol scaffolds can be produced by additive manufacturing.

Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2014-01-01

Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

A Regularized Approach for Solving Magnetic Differential Equations and a Revised Iterative Equilibrium Algorithm

International Nuclear Information System (INIS)

Hudson, S.R.

2010-01-01

A method for approximately solving magnetic differential equations is described. The approach is to include a small diffusion term to the equation, which regularizes the linear operator to be inverted. The extra term allows a 'source-correction' term to be defined, which is generally required in order to satisfy the solvability conditions. The approach is described in the context of computing the pressure and parallel currents in the iterative approach for computing magnetohydrodynamic equilibria.

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

Science.gov (United States)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

T-Stability of the Heun Method and Balanced Method for Solving Stochastic Differential Delay Equations

Directory of Open Access Journals (Sweden)

Xiaolin Zhu

2014-01-01

Full Text Available This paper studies the T-stability of the Heun method and balanced method for solving stochastic differential delay equations (SDDEs. Two T-stable conditions of the Heun method are obtained for two kinds of linear SDDEs. Moreover, two conditions under which the balanced method is T-stable are obtained for two kinds of linear SDDEs. Some numerical examples verify the theoretical results proposed.

A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

International Nuclear Information System (INIS)

Feng Qing-Hua

2014-01-01

In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

Computational singular perturbation analysis of stochastic chemical systems with stiffness

Science.gov (United States)

Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.

2017-04-01

Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

2016-02-15

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

On the application of subcell resolution to conservation laws with stiff source terms

International Nuclear Information System (INIS)

Chang, S.

1989-11-01

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented

The Adomian decomposition method for solving partial differential equations of fractal order in finite domains

Energy Technology Data Exchange (ETDEWEB)

El-Sayed, A.M.A. [Faculty of Science University of Alexandria (Egypt)]. E-mail: amasyed@hotmail.com; Gaber, M. [Faculty of Education Al-Arish, Suez Canal University (Egypt)]. E-mail: mghf408@hotmail.com

2006-11-20

The Adomian decomposition method has been successively used to find the explicit and numerical solutions of the time fractional partial differential equations. A different examples of special interest with fractional time and space derivatives of order {alpha}, 0<{alpha}=<1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of {alpha} are shown graphically for some examples.

Automatic differentiation bibliography

Energy Technology Data Exchange (ETDEWEB)

Corliss, G.F. [comp.

1992-07-01

This is a bibliography of work related to automatic differentiation. Automatic differentiation is a technique for the fast, accurate propagation of derivative values using the chain rule. It is neither symbolic nor numeric. Automatic differentiation is a fundamental tool for scientific computation, with applications in optimization, nonlinear equations, nonlinear least squares approximation, stiff ordinary differential equation, partial differential equations, continuation methods, and sensitivity analysis. This report is an updated version of the bibliography which originally appeared in Automatic Differentiation of Algorithms: Theory, Implementation, and Application.

The dependence of MG63 osteoblast responses to (meth)acrylate-based networks on chemical structure and stiffness.

Science.gov (United States)

Smith, Kathryn E; Hyzy, Sharon L; Sunwoo, Moonhae; Gall, Ken A; Schwartz, Zvi; Boyan, Barbara D

2010-08-01

The cell response to an implant is regulated by the implant's surface properties including topography and chemistry, but less is known about how the mechanical properties affect cell behavior. The objective of this study was to evaluate how the surface stiffness and chemistry of acrylate-based copolymer networks affect the in vitro response of human MG63 pre-osteoblast cells. Networks comprised of poly(ethylene glycol) dimethacrylate (PEGDMA; Mn approximately 750) and diethylene glycol dimethacrylate (DEGDMA) were photopolymerized at different concentrations to produce three compositions with moduli ranging from 850 to 60 MPa. To further decouple chemistry and stiffness, three networks comprised of 2-hydroxyethyl methacrylate (2HEMA) and PEGDMA or DEGDMA were also designed that exhibited a range of moduli similar to the PEGDMA-DEGDMA networks. MG63 cells were cultured on each surface and tissue culture polystyrene (TCPS), and the effect of copolymer composition on cell number, osteogenic markers (alkaline phosphatase specific activity and osteocalcin), and local growth factor production (OPG, TGF-beta1, and VEGF-A) were assessed. Cells exhibited a more differentiated phenotype on the PEGDMA-DEGDMA copolymers compared to the 2HEMA-PEGDMA copolymers. On the PEGDMA-DEGDMA system, cells exhibited a more differentiated phenotype on the stiffest surface indicated by elevated osteocalcin compared with TCPS. Conversely, cells on 2HEMA-PEGDMA copolymers became more differentiated on the less stiff 2HEMA surface. Growth factors were regulated in a differential manner. These results indicate that copolymer chemistry is the primary regulator of osteoblast differentiation, and the effect of stiffness is secondary to the surface chemistry. 2010 Elsevier Ltd. All rights reserved.

An Approach to Evaluate Stability for Cable-Based Parallel Camera Robots with Hybrid Tension-Stiffness Properties

Directory of Open Access Journals (Sweden)

Huiling Wei

2015-12-01

Full Text Available This paper focuses on studying the effect of cable tensions and stiffness on the stability of cable-based parallel camera robots. For this purpose, the tension factor and the stiffness factor are defined, and the expression of stability is deduced. A new approach is proposed to calculate the hybrid-stability index with the minimum cable tension and the minimum singular value. Firstly, the kinematic model of a cable-based parallel camera robot is established. Based on the model, the tensions are solved and a tension factor is defined. In order to obtain the tension factor, an optimization of the cable tensions is carried out. Then, an expression of the system's stiffness is deduced and a stiffness factor is defined. Furthermore, an approach to evaluate the stability of the cable-based camera robots with hybrid tension-stiffness properties is presented. Finally, a typical three-degree-of-freedom cable-based parallel camera robot with four cables is studied as a numerical example. The simulation results show that the approach is both reasonable and effective.

Limit cycles and stiffness control with variable stiffness actuators

NARCIS (Netherlands)

Carloni, Raffaella; Marconi, L.

2012-01-01

Variable stiffness actuators realize highly dynamic systems, whose inherent mechanical compliance can be properly exploited to obtain a robust and energy-efficient behavior. The paper presents a control strategy for variable stiffness actuators with the primarily goal of tracking a limit cycle

Effective computation of stochastic protein kinetic equation by reducing stiffness via variable transformation

Energy Technology Data Exchange (ETDEWEB)

Wang, Lijin, E-mail: ljwang@ucas.ac.cn [School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049 (China)

2016-06-08

The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.

Spectral finite element methods for solving fractional differential equations with applications in anomalous transport

Energy Technology Data Exchange (ETDEWEB)

Carella, Alfredo Raul

2012-09-15

Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)

When problem size matters: differential effects of brain stimulation on arithmetic problem solving and neural oscillations.

Directory of Open Access Journals (Sweden)

Bruno Rütsche

Full Text Available The problem size effect is a well-established finding in arithmetic problem solving and is characterized by worse performance in problems with larger compared to smaller operand size. Solving small and large arithmetic problems has also been shown to involve different cognitive processes and distinct electroencephalography (EEG oscillations over the left posterior parietal cortex (LPPC. In this study, we aimed to provide further evidence for these dissociations by using transcranial direct current stimulation (tDCS. Participants underwent anodal (30min, 1.5 mA, LPPC and sham tDCS. After the stimulation, we recorded their neural activity using EEG while the participants solved small and large arithmetic problems. We found that the tDCS effects on performance and oscillatory activity critically depended on the problem size. While anodal tDCS improved response latencies in large arithmetic problems, it decreased solution rates in small arithmetic problems. Likewise, the lower-alpha desynchronization in large problems increased, whereas the theta synchronization in small problems decreased. These findings reveal that the LPPC is differentially involved in solving small and large arithmetic problems and demonstrate that the effects of brain stimulation strikingly differ depending on the involved neuro-cognitive processes.

ADAPTIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS VIA NATURAL EMBEDDINGS AND REJECTION SAMPLING WITH MEMORY.

Science.gov (United States)

Rackauckas, Christopher; Nie, Qing

2017-01-01

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs.

A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations

Directory of Open Access Journals (Sweden)

F. Ghomanjani

2016-10-01

Full Text Available In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.

Development of a stiffness-angle law for simplifying the measurement of human hair stiffness.

Science.gov (United States)

Jung, I K; Park, S C; Lee, Y R; Bin, S A; Hong, Y D; Eun, D; Lee, J H; Roh, Y S; Kim, B M

2018-04-01

This research examines the benefits of caffeine absorption on hair stiffness. To test hair stiffness, we have developed an evaluation method that is not only accurate, but also inexpensive. Our evaluation method for measuring hair stiffness culminated in a model, called the Stiffness-Angle Law, which describes the elastic properties of hair and can be widely applied to the development of hair care products. Small molecules (≤500 g mol -1 ) such as caffeine can be absorbed into hair. A common shampoo containing 4% caffeine was formulated and applied to hair 10 times, after which the hair stiffness was measured. The caffeine absorption of the treated hair was observed using Fourier-transform infrared spectroscopy (FTIR) with a focal plane array (FPA) detector. Our evaluation method for measuring hair stiffness consists of a regular camera and a support for single strands of hair. After attaching the hair to the support, the bending angle of the hair was observed with a camera and measured. Then, the hair strand was weighed. The stiffness of the hair was calculated based on our proposed Stiffness-Angle Law using three variables: angle, weight of hair and the distance the hair was pulled across the support. The caffeine absorption was confirmed by FTIR analysis. The concentration of amide bond in the hair certainly increased due to caffeine absorption. After caffeine was absorbed into the hair, the bending angle and weight of the hair changed. Applying these measured changes to the Stiffness-Angle Law, it was confirmed that the hair stiffness increased by 13.2% due to caffeine absorption. The theoretical results using the Stiffness-Angle Law agree with the visual examinations of hair exposed to caffeine and also the known results of hair stiffness from a previous report. Our evaluation method combined with our proposed Stiffness-Angle Law effectively provides an accurate and inexpensive evaluation technique for measuring bending stiffness of human hair. © 2018

Elastic dynamic research of high speed multi-link precision press considering structural stiffness of rotation joints

Energy Technology Data Exchange (ETDEWEB)

Hu, Feng Feng; Sun, Yu; Peng, Bin Bin [School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing (China)

2016-10-15

An elastic dynamic model of high-speed multi-link precision press considering structural stiffness of rotation joints was established by the finite element method. In the finite element model, rotation joint was established by four bar elements with equivalent stiffness, and connected link was established by beam element. Then, the elastic dynamics equation of the system was established, and modal superposition method was used to solve the dynamic response. Compared with the traditional elastic dynamic model with perfect constraint of the rotation joints, the elastic dynamic response value of the improved model is larger. To validate the presented new method of elastic dynamics analysis with stiffness of rotation joints, a related test of slider Bottom dead center (BDC) position in different speed was designed. The test shows that the model with stiffness of rotation joints is more reasonable. So it provides a reasonable theory and method for dynamic characteristics research of such a multi-link machine.

Posttraumatic stiff elbow

Directory of Open Access Journals (Sweden)

Ravi Mittal

2017-01-01

Full Text Available Posttraumatic stiff elbow is a frequent and disabling complication and poses serious challenges for its management. In this review forty studies were included to know about the magnitude of the problem, causes, pathology, prevention, and treatment of posttraumatic stiff elbow. These studies show that simple measures such as internal fixation, immobilization in extension, and early motion of elbow joint are the most important steps that can prevent elbow stiffness. It also supports conservative treatment in selected cases. There are no clear guidelines about the choice between the numerous procedures described in literature. However, this review article disproves two major beliefs-heterotopic ossification is a bad prognostic feature, and passive mobilization of elbow causes elbow stiffness.

Give me a hand: Differential effects of gesture type in guiding young children's problem-solving

OpenAIRE

Vallotton, Claire; Fusaro, Maria; Hayden, Julia; Decker, Kalli; Gutowski, Elizabeth

2015-01-01

Adults’ gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents’ use of gestures to support their young children (1.5 – 6 years) in a block puzzle task (N = 126 parent-child dyads), and identified patterns in parents’ gesture use indicating different gestural strategies. Further, we examined the...

Fibonacci collocation method with a residual error Function to solve linear Volterra integro differential equations

Directory of Open Access Journals (Sweden)

Salih Yalcinbas

2016-01-01

Full Text Available In this paper, a new collocation method based on the Fibonacci polynomials is introduced to solve the high-order linear Volterra integro-differential equations under the conditions. Numerical examples are included to demonstrate the applicability and validity of the proposed method and comparisons are made with the existing results. In addition, an error estimation based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation.

Homotopy perturbation transform method for pricing under pure diffusion models with affine coefficients

Directory of Open Access Journals (Sweden)

Claude Rodrigue Bambe Moutsinga

2018-01-01

Full Text Available Most existing multivariate models in finance are based on diffusion models. These models typically lead to the need of solving systems of Riccati differential equations. In this paper, we introduce an efficient method for solving systems of stiff Riccati differential equations. In this technique, a combination of Laplace transform and homotopy perturbation methods is considered as an algorithm to the exact solution of the nonlinear Riccati equations. The resulting technique is applied to solving stiff diffusion model problems that include interest rates models as well as two and three-factor stochastic volatility models. We show that the present approach is relatively easy, efficient and highly accurate.

Comparison of magnetic resonance elastography and diffusion-weighted imaging for differentiating benign and malignant liver lesions.

Science.gov (United States)

Hennedige, Tiffany P; Hallinan, James Thomas Patrick Decourcy; Leung, Fiona P; Teo, Lynette Li San; Iyer, Sridhar; Wang, Gang; Chang, Stephen; Madhavan, Krishna Kumar; Wee, Aileen; Venkatesh, Sudhakar K

2016-02-01

Comparison of magnetic resonance elastography (MRE) and diffusion-weighted imaging (DWI) for differentiating malignant and benign focal liver lesions (FLLs). Seventy-nine subjects with 124 FLLs (44 benign and 80 malignant) underwent both MRE and DWI. MRE was performed with a modified gradient-echo sequence and DWI with a free breathing technique (b = 0.500). Apparent diffusion coefficient (ADC) maps and stiffness maps were generated. FLL mean stiffness and ADC values were obtained by placing regions of interest over the FLLs on stiffness and ADC maps. The accuracy of MRE and DWI for differentiation of benign and malignant FLL was compared using receiver operating curve (ROC) analysis. There was a significant negative correlation between stiffness and ADC (r = -0.54, p 4.54kPa) and DWI (cut-off, benign and malignant FLLs. • MRE is superior to DWI for differentiating benign and malignant focal liver lesions. • Benign lesions with large fibrous components may have higher stiffness with MRE. • Cholangiocarcinomas tend to have higher stiffness than hepatocellular carcinomas. • Hepatocellular adenomas tend to have lower stiffness than focal nodular hyperplasia. • MRE is superior to conventional MRI in differentiating benign and malignant liver lesions.

Macrophage involvement affects matrix stiffness-related influences on cell osteogenesis under three-dimensional culture conditions.

Science.gov (United States)

He, Xiao-Tao; Wu, Rui-Xin; Xu, Xin-Yue; Wang, Jia; Yin, Yuan; Chen, Fa-Ming

2018-04-15

Accumulating evidence indicates that the physicochemical properties of biomaterials exert profound influences on stem cell fate decisions. However, matrix-based regulation selected through in vitro analyses based on a given cell population do not genuinely reflect the in vivo conditions, in which multiple cell types are involved and interact dynamically. This study constitutes the first investigation of how macrophages (Mφs) in stiffness-tunable transglutaminase cross-linked gelatin (TG-gel) affect the osteogenesis of bone marrow-derived mesenchymal stem cells (BMMSCs). When a single cell type was cultured, low-stiffness TG-gels promoted BMMSC proliferation, whereas high-stiffness TG-gels supported cell osteogenic differentiation. However, Mφs in high-stiffness TG-gels were more likely to polarize toward the pro-inflammatory M1 phenotype. Using either conditioned medium (CM)-based incubation or Transwell-based co-culture, we found that Mφs encapsulated in the low-stiffness matrix exerted a positive effect on the osteogenesis of co-cultured BMMSCs. Conversely, Mφs in high-stiffness TG-gels negatively affected cell osteogenic differentiation. When both cell types were cultured in the same TG-gel type and placed into the Transwell system, the stiffness-related influences of Mφs on BMMSCs were significantly altered; both the low- and high-stiffness matrix induced similar levels of BMMSC osteogenesis. Although the best material parameter for synergistically affecting Mφs and BMMSCs remains unknown, our data suggest that Mφ involvement in the co-culture system alters previously identified material-related influences on BMMSCs, such as matrix stiffness-related effects, which were identified based on a culture system involving a single cell type. Such Mφ-stem cell interactions should be considered when establishing proper matrix parameter-associated cell regulation in the development of biomimetic biomaterials for regenerative applications. The substrate stiffness

The effect of vocal fold vertical stiffness gradient on sound production

Science.gov (United States)

Geng, Biao; Xue, Qian; Zheng, Xudong

2015-11-01

It is observed in some experimental studies on canine vocal folds (VFs) that the inferior aspect of the vocal fold (VF) is much stiffer than the superior aspect under relatively large strain. Such vertical difference is supposed to promote the convergent-divergent shape during VF vibration and consequently facilitate the production of sound. In this study, we investigate the effect of vertical variation of VF stiffness on sound production using a numerical model. The vertical variation of stiffness is produced by linearly increasing the Young's modulus and shear modulus from the superior to inferior aspects in the cover layer, and its effect on phonation is examined in terms of aerodynamic and acoustic quantities such as flow rate, open quotient, skewness of flow wave form, sound intensity and vocal efficiency. The flow-induced vibration of the VF is solved with a finite element solver coupled with 1D Bernoulli equation, which is further coupled with a digital waveguide model. This study is designed to find out whether it's beneficial to artificially induce the vertical stiffness gradient by certain implanting material in VF restoring surgery, and if it is beneficial, what gradient is the most favorable.

Enhanced Differentiation of Human Embryonic Stem Cells Toward Definitive Endoderm on Ultrahigh Aspect Ratio Nanopillars

DEFF Research Database (Denmark)

Rasmussen, Camilla Holzmann; Reynolds, Paul M.; Petersen, Dorthe Roenn

2016-01-01

highlighted that the properties of the physical environment, such as substrate stiffness, affect cellular behavior. Here, mass-produced, injection molded polycarbonate nanopillars are presented, where the surface mechanical properties, i.e., stiffness, can be controlled by the geometric design...... of the ultrahigh aspect ratio nanopillars (stiffness can be reduced by 25.000X). It is found that tall nanopillars, yielding softer surfaces, significantly enhance the induction of defi nitive endoderm cells from pluripotent human embryonic stem cells, resulting in more consistent differentiation of a pure...... population compared to planar control. By contrast, further differentiation toward the pancreatic endoderm is less successful on “soft” pillars when compared to “stiff ” pillars or control, indicating differential cues during the different stages of differentiation. To accompany the mechanical properties...

Arterial stiffness and cognitive impairment.

Science.gov (United States)

Li, Xiaoxuan; Lyu, Peiyuan; Ren, Yanyan; An, Jin; Dong, Yanhong

2017-09-15

Arterial stiffness is one of the earliest indicators of changes in vascular wall structure and function and may be assessed using various indicators, such as pulse-wave velocity (PWV), the cardio-ankle vascular index (CAVI), the ankle-brachial index (ABI), pulse pressure (PP), the augmentation index (AI), flow-mediated dilation (FMD), carotid intima media thickness (IMT) and arterial stiffness index-β. Arterial stiffness is generally considered an independent predictor of cardiovascular and cerebrovascular diseases. To date, a significant number of studies have focused on the relationship between arterial stiffness and cognitive impairment. To investigate the relationships between specific arterial stiffness parameters and cognitive impairment, elucidate the pathophysiological mechanisms underlying the relationship between arterial stiffness and cognitive impairment and determine how to interfere with arterial stiffness to prevent cognitive impairment, we searched PUBMED for studies regarding the relationship between arterial stiffness and cognitive impairment that were published from 2000 to 2017. We used the following key words in our search: "arterial stiffness and cognitive impairment" and "arterial stiffness and cognitive impairment mechanism". Studies involving human subjects older than 30years were included in the review, while irrelevant studies (i.e., studies involving subjects with comorbid kidney disease, diabetes and cardiac disease) were excluded from the review. We determined that arterial stiffness severity was positively correlated with cognitive impairment. Of the markers used to assess arterial stiffness, a higher PWV, CAVI, AI, IMT and index-β and a lower ABI and FMD were related to cognitive impairment. However, the relationship between PP and cognitive impairment remained controversial. The potential mechanisms linking arterial stiffness and cognitive impairment may be associated with arterial pulsatility, as greater arterial pulsatility

Impact of morning stiffness on working behaviour and performance in people with rheumatoid arthritis.

Science.gov (United States)

Mattila, Kalle; Buttgereit, Frank; Tuominen, Risto

2014-12-01

Work disability remains a considerable problem for many patients with rheumatoid arthritis (RA). Morning stiffness is a symptom of RA associated with early retirement from work and with impaired functional ability. We aimed to explore the patient's perception of the impact of morning stiffness on the working life of patients with RA. A survey was conducted in 11 European countries. Patients of working age, with RA for ≥6 months and morning stiffness ≥3 mornings a week, were interviewed by telephone using a structured questionnaire. Responses were assessed in the total sample and in subgroups defined by severity and duration of morning stiffness and by country. A total of 1,061 respondents completed the survey, 534 were working, 224 were retired and the rest were, i.e. homemakers and unemployed. Among the 534 working respondents, RA-related morning stiffness affected work performance (47 %), resulted in late arrival at work (33 %) and required sick leave in the past month (15 %). Of the 224 retired respondents, 159 (71 %) stopped working earlier than their expected retirement age, with 64 % giving RA-related morning stiffness as a reason. There was a differential impact of increasing severity and increasing duration of morning stiffness on the various parameters studied. There were notable inter-country differences in the impact of RA-related morning stiffness on ability to work and on retirement. This large survey showed that from the patient's perspective, morning stiffness reduces the ability to work in patients with RA and contributes to early retirement.

Hemodynamic and arterial stiffness differences between African-Americans and Caucasians after maximal exercise.

Science.gov (United States)

Yan, Huimin; Ranadive, Sushant M; Heffernan, Kevin S; Lane, Abbi D; Kappus, Rebecca M; Cook, Marc D; Wu, Pei-Tzu; Sun, Peng; Harvey, Idethia S; Woods, Jeffrey A; Wilund, Kenneth R; Fernhall, Bo

2014-01-01

African-American (AA) men have higher arterial stiffness and augmentation index (AIx) than Caucasian-American (CA) men. Women have greater age-associated increases in arterial stiffness and AIx than men. This study examined racial and sex differences in arterial stiffness and central hemodynamics at rest and after an acute bout of maximal exercise in young healthy individuals. One hundred young, healthy individuals (28 AA men, 24 AA women, 25 CA men, and 23 CA women) underwent measurements of aortic blood pressure (BP) and arterial stiffness at rest and 15 and 30 min after an acute bout of graded maximal aerobic exercise. Aortic BP and AIx were derived from radial artery applanation tonometry. Aortic stiffness (carotid-femoral) was measured via pulse wave velocity. Aortic stiffness was increased in AA subjects but not in CA subjects (P < 0.05) after an acute bout of maximal cycling exercise, after controlling for body mass index. Aortic BP decreased after exercise in CA subjects but not in AA subjects (P < 0.05). Women exhibited greater reductions in AIx after maximal aerobic exercise compared with men (P < 0.05). In conclusion, race and sex impact vascular and central hemodynamic responses to exercise. Young AA and CA subjects exhibited differential responses in central stiffness and central BP after acute maximal exercise. Premenopausal women had greater augmented pressure at rest and after maximal aerobic exercise than men. Future research is needed to examine the potential mechanisms.

Estimating Gear Teeth Stiffness

DEFF Research Database (Denmark)

Pedersen, Niels Leergaard

2013-01-01

The estimation of gear stiffness is important for determining the load distribution between the gear teeth when two sets of teeth are in contact. Two factors have a major influence on the stiffness; firstly the boundary condition through the gear rim size included in the stiffness calculation...... and secondly the size of the contact. In the FE calculation the true gear tooth root profile is applied. The meshing stiffness’s of gears are highly non-linear, it is however found that the stiffness of an individual tooth can be expressed in a linear form assuming that the contact length is constant....

An investigation into the accuracy, stability and parallel performance of a highly stable explicit technique for stiff reaction-transport PDEs

Energy Technology Data Exchange (ETDEWEB)

Franz, A., LLNL

1998-02-17

The numerical simulation of chemically reacting flows is a topic, that has attracted a great deal of current research At the heart of numerical reactive flow simulations are large sets of coupled, nonlinear Partial Differential Equations (PDES). Due to the stiffness that is usually present, explicit time differencing schemes are not used despite their inherent simplicity and efficiency on parallel and vector machines, since these schemes require prohibitively small numerical stepsizes. Implicit time differencing schemes, although possessing good stability characteristics, introduce a great deal of computational overhead necessary to solve the simultaneous algebraic system at each timestep. This thesis examines an algorithm based on a preconditioned time differencing scheme. The algorithm is explicit and permits a large stable time step. An investigation of the algorithm`s accuracy, stability and performance on a parallel architecture is presented

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

Science.gov (United States)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

Directory of Open Access Journals (Sweden)

Elhassan Eljaoui

2018-01-01

Full Text Available We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic.

Trabecular meshwork stiffness in glaucoma.

Science.gov (United States)

Wang, Ke; Read, A Thomas; Sulchek, Todd; Ethier, C Ross

2017-05-01

Alterations in stiffness of the trabecular meshwork (TM) may play an important role in primary open-angle glaucoma (POAG), the second leading cause of blindness. Specifically, certain data suggest an association between elevated intraocular pressure (IOP) and increased TM stiffness; however, the underlying link between TM stiffness and IOP remains unclear and requires further study. We here first review the literature on TM stiffness measurements, encompassing various species and based on a number of measurement techniques, including direct approaches such as atomic force microscopy (AFM) and uniaxial tension tests, and indirect methods based on a beam deflection model. We also briefly review the effects of several factors that affect TM stiffness, including lysophospholipids, rho-kinase inhibitors, cytoskeletal disrupting agents, dexamethasone (DEX), transforming growth factor-β 2 (TGF-β 2 ), nitric oxide (NO) and cellular senescence. We then describe a method we have developed for determining TM stiffness measurement in mice using a cryosection/AFM-based approach, and present preliminary data on TM stiffness in C57BL/6J and CBA/J mouse strains. Finally, we investigate the relationship between TM stiffness and outflow facility between these two strains. The method we have developed shows promise for further direct measurements of mouse TM stiffness, which may be of value in understanding mechanistic relations between outflow facility and TM biomechanical properties. Copyright © 2016 Elsevier Ltd. All rights reserved.

Artificial muscles with adjustable stiffness

International Nuclear Information System (INIS)

Mutlu, Rahim; Alici, Gursel

2010-01-01

This paper reports on a stiffness enhancement methodology based on using a suitably designed contact surface with which cantilevered-type conducting polymer bending actuators are in contact during operation. The contact surface constrains the bending behaviour of the actuators. Depending on the topology of the contact surface, the resistance of the polymer actuators to deformation, i.e. stiffness, is varied. As opposed to their predecessors, these polymer actuators operate in air. Finite element analysis and modelling are used to quantify the effect of the contact surface on the effective stiffness of a trilayer cantilevered beam, which represents a one-end-free, the-other-end-fixed polypyrrole (PPy) conducting polymer actuator under a uniformly distributed load. After demonstrating the feasibility of the adjustable stiffness concept, experiments were conducted to determine the stiffness of bending-type conducting polymer actuators in contact with a range (20–40 mm in radius) of circular contact surfaces. The numerical and experimental results presented demonstrate that the stiffness of the actuators can be varied using a suitably profiled contact surface. The larger the radius of the contact surface is, the higher is the stiffness of the polymer actuators. The outcomes of this study suggest that, although the stiffness of the artificial muscles considered in this study is constant for a given geometric size, and electrical and chemical operation conditions, it can be changed in a nonlinear fashion to suit the stiffness requirement of a considered application. The stiffness enhancement methodology can be extended to other ionic-type conducting polymer actuators

A variable stiffness joint with electrospun P(VDF-TrFE-CTFE) variable stiffness springs

NARCIS (Netherlands)

Carloni, Raffaella; Lapp, Valerie I.; Cremonese, Andrea; Belcari, Juri; Zucchelli, Andrea

This letter presents a novel rotational variable stiffness joint that relies on one motor and a set of variable stiffness springs. The variable stiffness springs are leaf springs with a layered design, i.e., an electro-active layer of electrospun aligned nanofibers of poly(vinylidene

Pharmacological modulation of arterial stiffness.

LENUS (Irish Health Repository)

Boutouyrie, Pierre

2011-09-10

Arterial stiffness has emerged as an important marker of cardiovascular risk in various populations and reflects the cumulative effect of cardiovascular risk factors on large arteries, which in turn is modulated by genetic background. Arterial stiffness is determined by the composition of the arterial wall and the arrangement of these components, and can be studied in humans non-invasively. Age and distending pressure are two major factors influencing large artery stiffness. Change in arterial stiffness with drugs is an important endpoint in clinical trials, although evidence for arterial stiffness as a therapeutic target still needs to be confirmed. Drugs that independently affect arterial stiffness include antihypertensive drugs, mostly blockers of the renin-angiotensin-aldosterone system, hormone replacement therapy and some antidiabetic drugs such as glitazones. While the quest continues for \\'de-stiffening drugs\\

PSsolver: A Maple implementation to solve first order ordinary differential equations with Liouvillian solutions

Science.gov (United States)

Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.

2012-10-01

We present a set of software routines in Maple 14 for solving first order ordinary differential equations (FOODEs). The package implements the Prelle-Singer method in its original form together with its extension to include integrating factors in terms of elementary functions. The package also presents a theoretical extension to deal with all FOODEs presenting Liouvillian solutions. Applications to ODEs taken from standard references show that it solves ODEs which remain unsolved using Maple's standard ODE solution routines. New version program summary Program title: PSsolver Catalogue identifier: ADPR_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADPR_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2302 No. of bytes in distributed program, including test data, etc.: 31962 Distribution format: tar.gz Programming language: Maple 14 (also tested using Maple 15 and 16). Computer: Intel Pentium Processor P6000, 1.86 GHz. Operating system: Windows 7. RAM: 4 GB DDR3 Memory Classification: 4.3. Catalogue identifier of previous version: ADPR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 144 (2002) 46 Does the new version supersede the previous version?: Yes Nature of problem: Symbolic solution of first order differential equations via the Prelle-Singer method. Solution method: The method of solution is based on the standard Prelle-Singer method, with extensions for the cases when the FOODE contains elementary functions. Additionally, an extension of our own which solves FOODEs with Liouvillian solutions is included. Reasons for new version: The program was not running anymore due to changes in the latest versions of Maple. Additionally, we corrected/changed some bugs/details that were hampering the smoother functioning of the routines. Summary

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

Science.gov (United States)

Khader, M M

2013-10-01

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

Measurements of stiff-material compliance on the nanoscale using ultrasonic force microscopy

Science.gov (United States)

Dinelli, F.; Biswas, S. K.; Briggs, G. A. D.; Kolosov, O. V.

2000-05-01

Ultrasonic force microscopy (UFM) was introduced to probe nanoscale mechanical properties of stiff materials. This was achieved by vibrating the sample far above the first resonance of the probing atomic force microscope cantilever where the cantilever becomes dynamically rigid. By operating UFM at different set force values, it is possible to directly measure the absolute values of the tip-surface contact stiffness. From this an evaluation of surface elastic properties can be carried out assuming a suitable solid-solid contact model. In this paper we present curves of stiffness as a function of the normal load in the range of 0-300 nN. The dependence of stiffness on the relative humidity has also been investigated. Materials with different elastic constants (such as sapphire lithium fluoride, and silicon) have been successfully differentiated. Continuum mechanics models cannot however explain the dependence of stiffness on the normal force and on the relative humidity. In this high-frequency regime, it is likely that viscous forces might play an important role modifying the tip-surface interaction. Plastic deformation might also occur due to the high strain rates applied when ultrasonically vibrating the sample. Another possible cause of these discrepancies might be the presence of water in between the two bodies in contact organizing in a solidlike way and partially sustaining the load.

Dielectric metasurfaces solve differential and integro-differential equations.

Science.gov (United States)

Abdollahramezani, Sajjad; Chizari, Ata; Dorche, Ali Eshaghian; Jamali, Mohammad Vahid; Salehi, Jawad A

2017-04-01

Leveraging subwavelength resonant nanostructures, plasmonic metasurfaces have recently attracted much attention as a breakthrough concept for engineering optical waves both spatially and spectrally. However, inherent ohmic losses concomitant with low coupling efficiencies pose fundamental impediments over their practical applications. Not only can all-dielectric metasurfaces tackle such substantial drawbacks, but also their CMOS-compatible configurations support both Mie resonances that are invariant to the incident angle. Here, we report on a transmittive metasurface comprising arrayed silicon nanodisks embedded in a homogeneous dielectric medium to manipulate phase and amplitude of incident light locally and almost independently. By taking advantage of the interplay between the electric/magnetic resonances and employing general concepts of spatial Fourier transformation, a highly efficient metadevice is proposed to perform mathematical operations including solution of ordinary differential and integro-differential equations with constant coefficients. Our findings further substantiate dielectric metasurfaces as promising candidates for miniaturized, two-dimensional, and planar optical analog computing systems that are much thinner than their conventional lens-based counterparts.

Solving Differential Equations in R

Science.gov (United States)

Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here w...

Differentiation between non-neural and neural contributors to ankle joint stiffness in cerebral palsy

NARCIS (Netherlands)

De Gooijer-van de Groep, K.L.; De Vlugt, E.; De Groot, J.H.; Van der Heijden-Maessen, H.C.M.; Wielheesen, D.H.M.; Van Wijlen-Hempel, R.M.S.; Arendzen, J.H.; Meskers, C.G.M.

2013-01-01

Background Spastic paresis in cerebral palsy (CP) is characterized by increased joint stiffness that may be of neural origin, i.e. improper muscle activation caused by e.g. hyperreflexia or non-neural origin, i.e. altered tissue viscoelastic properties (clinically: “spasticity” vs. “contracture”).

Measurement and Treatment of Passive Muscle Stiffness

DEFF Research Database (Denmark)

Kirk, Henrik

, which aimed to investigate: 1) The development of a clinical method to evaluate and distinguish neural (reflex mediated stiffness) and non-neural (passive muscle stiffness) components of muscle stiffness in adults with CP by objective and reliable measurements. 2) The association between increased...... and reliability of the method, and argue for the use of the method in the clinical practice. The device is able to distinguish between passive muscle stiffness and reflex-mediated stiffness in subjects with CP. It shows good high intrarater and interrater reliability in evaluation of passive muscle stiffness...... to measure muscle stiffness, and distinguish between passive muscle stiffness and reflex-mediated stiffness. Furthermore, it is a reliable device to measure changes in passive ROM. Treatment of passive muscle stiffness should be directed towards intense training, comprising many repetitions with a functional...

A Special Family of LMM with Two Hybrid Points for Stiff ODEs ...

African Journals Online (AJOL)

Enright (1974) discussed the formulation of the second derivative LMM which was found to be stiffly stable for step number k £ 7 for the numerical solution of stiff Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs). In this paper some second derivative continuous linear multistep methods with two hybrid ...

Effective quadrature formula in solving linear integro-differential equations of order two

Science.gov (United States)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

On gear tooth stiffness evaluation

DEFF Research Database (Denmark)

Pedersen, Niels Leergaard; Jørgensen, Martin Felix

2014-01-01

The estimation of gear stiffness is important for determining the load distribution between the gear teeth when two sets of teeth are in contact. Two factors have a major influence on the stiffness; firstly the boundary condition through the gear rim size included in the stiffness calculation...

Recent symbolic summation methods to solve coupled systems of differential and difference equations

International Nuclear Information System (INIS)

Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de

2014-07-01

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.

Recent symbolic summation methods to solve coupled systems of differential and difference equations

Energy Technology Data Exchange (ETDEWEB)

Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Freitas, Abilio de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2014-07-15

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.

Stiff person syndrome (SPS: Literature review and case report

Directory of Open Access Journals (Sweden)

Erna Pretorius

2013-11-01

Full Text Available Stiff person syndrome (SPS is a rare, debilitating condition which presents with progressive and inconsistent neurological features. The main symptoms are stiffness and intermittent, painful muscle spasms, triggered and exacerbated by stressful and emotional stimuli. The fluctuating clinical nature of SPS, and otherwise normal neurological examination, often lead to a misdiagnosis of conversion disorder. Psychiatric symptoms frequently accompany this disorder and patients are often first seen by psychiatrists. SPS is autoimmune-based: antibodies are directed against glutamate decarboxylase, resulting in dysregulation of gamma-aminobutyric acid (GABA in the brain which is considered the cause of the neuropsychiatric symptomatology. SPS should be considered in the differential diagnosis of conversion disorder. Effective management requires early detection, a collaborative approach with GABA-ergic medication and intravenous immunoglobulins, and management of concomitant psychiatric disorders. We describe a patient with SPS. Only one other case has been reported in South Africa.

Dynamic stiffness of suction caissons

DEFF Research Database (Denmark)

Ibsen, Lars Bo; Liingaard, Morten; Andersen, Lars

The purpose of this report is to evaluate the dynamic soil-structure interaction of suction caissons for offshore wind turbines. The investigation is limited to a determination of the vertical dynamic stiffness of suction caissons. The soil surrounding the foundation is homogenous with linear...... viscoelastic properties. The dynamic stiffness of the suction caisson is expressed by dimensionless frequency-dependent dynamic stiffness coefficients corresponding to the vertical degree of freedom. The dynamic stiffness coefficients for the foundations are evaluated by means of a dynamic three...

A simple indentation device for measuring micrometer-scale tissue stiffness

Energy Technology Data Exchange (ETDEWEB)

Levental, I; Levental, K R; Janmey, P A [Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia, PA 19104 (United States); Klein, E A; Assoian, R [Department of Pharmacology, University of Pennsylvania, Philadelphia, PA 19104 (United States); Miller, R T [Departments of Medicine and Physiology, Louis Stokes VAMC, Cleveland, OH (United States); Wells, R G, E-mail: janmey@mail.med.upenn.ed [Department of Medicine, University of Pennsylvania, Philadelphia, PA 19104 (United States)

2010-05-19

Mechanical properties of cells and extracellular matrices are critical determinants of function in contexts including oncogenic transformation, neuronal synapse formation, hepatic fibrosis and stem cell differentiation. The size and heterogeneity of biological specimens and the importance of measuring their mechanical properties under conditions that resemble their environments in vivo present a challenge for quantitative measurement. Centimeter-scale tissue samples can be measured by commercial instruments, whereas properties at the subcellular (nm) scale are accessible by atomic force microscopy, optical trapping, or magnetic bead microrheometry; however many tissues are heterogeneous on a length scale between micrometers and millimeters which is not accessible to most current instrumentation. The device described here combines two commercially available technologies, a micronewton resolution force probe and a micromanipulator for probing soft biological samples at sub-millimeter spatial resolution. Several applications of the device are described. These include the first measurement of the stiffness of an intact, isolated mouse glomerulus, quantification of the inner wall stiffness of healthy and diseased mouse aortas, and evaluation of the lateral heterogeneity in the stiffness of mouse mammary glands and rat livers with correlation of this heterogeneity with malignant or fibrotic pathology as evaluated by histology.

A universal concept based on cellular neural networks for ultrafast and flexible solving of differential equations.

Science.gov (United States)

Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere

2015-04-01

This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.

Solving Nonlinear Coupled Differential Equations

Science.gov (United States)

Mitchell, L.; David, J.

1986-01-01

Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

Generalized differential transform method to differential-difference equation

International Nuclear Information System (INIS)

Zou Li; Wang Zhen; Zong Zhi

2009-01-01

In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Pade technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation.

Variable-mesh method of solving differential equations

Science.gov (United States)

Van Wyk, R.

1969-01-01

Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations.

Solving Differential Equations Using Modified Picard Iteration

Science.gov (United States)

Robin, W. A.

2010-01-01

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

Solving variational problems and partial differential equations that map between manifolds via the closest point method

Science.gov (United States)

King, Nathan D.; Ruuth, Steven J.

2017-05-01

Maps from a source manifold M to a target manifold N appear in liquid crystals, color image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems and partial differential equations (PDEs) that map between manifolds is introduced within this paper. Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N. This enables the use of standard Cartesian numerics for general manifolds that are open or closed, with or without orientation, and of any codimension. An algorithm is presented for the important example of harmonic maps and generalized to a broader class of PDEs, which includes p-harmonic maps. Improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods. Harmonic and p-harmonic maps are computed for a variety of numerical examples. In these examples, we denoise texture maps, diffuse random maps between general manifolds, and enhance color images.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

Science.gov (United States)

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Properties and determination of the interface stiffness

International Nuclear Information System (INIS)

Du Danxu; Zhang Hao; Srolovitz, David J.

2007-01-01

The chemical potential of a curved interface contains a term that is proportional to the product of the interface curvature and the interface stiffness. In crystalline materials, the interface stiffness is a tensor. This paper examines several basic issues related to the properties of the interface stiffness, especially the determination of the interface stiffness in particular directions (i.e. the commonly used scalar form of the interface stiffness). Of the five parameters that describe an arbitrary grain boundary, only those describing the inclination are crucial for the scalar stiffness. We also examine the influence of crystal symmetry on the stiffness tensor for both free surfaces and grain boundaries. This results in substantial simplifications for cases in which interfaces possess mirror or rotational symmetries. An efficient method for determining the interface stiffness tensor using atomistic simulations is proposed

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

Science.gov (United States)

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

A Novel Variable Stiffness Mechanism Capable of an Infinite Stiffness Range and Unlimited Decoupled Output Motion

Directory of Open Access Journals (Sweden)

Stefan Groothuis

2014-06-01

Full Text Available In this paper, a novel variable stiffness mechanism is presented, which is capable of achieving an output stiffness with infinite range and an unlimited output motion, i.e., the mechanism output is completely decoupled from the rotor motion, in the zero stiffness configuration. The mechanism makes use of leaf springs, which are engaged at different positions by means of two movable supports, to realize the variable output stiffness. The Euler–Bernoulli leaf spring model is derived and validated through experimental data. By shaping the leaf springs, it is shown that the stiffness characteristic of the mechanism can be changed to fulfill different application requirements. Alternative designs can achieve the same behavior with only one leaf spring and one movable support pin.

Stiffness of desiccating insect wings

International Nuclear Information System (INIS)

Mengesha, T E; Vallance, R R; Mittal, R

2011-01-01

The stiffness of insect wings is typically determined through experimental measurements. Such experiments are performed on wings removed from insects. However, the wings are subject to desiccation which typically leads to an increase in their stiffness. Although this effect of desiccation is well known, a comprehensive study of the rate of change in stiffness of desiccating insect wings would be a significant aid in planning experiments as well as interpreting data from such experiments. This communication presents a comprehensive experimental analysis of the change in mass and stiffness of gradually desiccating forewings of Painted Lady butterflies (Vanessa cardui). Mass and stiffness of the forewings of five butterflies were simultaneously measured every 10 min over a 24 h period. The averaged results show that wing mass declined exponentially by 21.1% over this time period with a time constant of 9.8 h, while wing stiffness increased linearly by 46.2% at a rate of 23.4 μN mm -1 h -1 . For the forewings of a single butterfly, the experiment was performed over a period of 1 week, and the results show that wing mass declined exponentially by 52.2% with a time constant of 30.2 h until it reached a steady-state level of 2.00 mg, while wing stiffness increased exponentially by 90.7% until it reached a steady-state level of 1.70 mN mm -1 . (communication)

Stiffness of desiccating insect wings

Energy Technology Data Exchange (ETDEWEB)

Mengesha, T E; Vallance, R R [Department of Mechanical Engineering, The George Washington University, 738 Phillips Hall, 801 22nd St NW, Washington, DC 20052 (United States); Mittal, R, E-mail: vallance@gwu.edu [Department of Mechanical Engineering, Johns Hopkins University, 126 Latrobe Hall, 3400 N Charles Street, Baltimore, MD 21218 (United States)

2011-03-15

The stiffness of insect wings is typically determined through experimental measurements. Such experiments are performed on wings removed from insects. However, the wings are subject to desiccation which typically leads to an increase in their stiffness. Although this effect of desiccation is well known, a comprehensive study of the rate of change in stiffness of desiccating insect wings would be a significant aid in planning experiments as well as interpreting data from such experiments. This communication presents a comprehensive experimental analysis of the change in mass and stiffness of gradually desiccating forewings of Painted Lady butterflies (Vanessa cardui). Mass and stiffness of the forewings of five butterflies were simultaneously measured every 10 min over a 24 h period. The averaged results show that wing mass declined exponentially by 21.1% over this time period with a time constant of 9.8 h, while wing stiffness increased linearly by 46.2% at a rate of 23.4 {mu}N mm{sup -1} h{sup -1}. For the forewings of a single butterfly, the experiment was performed over a period of 1 week, and the results show that wing mass declined exponentially by 52.2% with a time constant of 30.2 h until it reached a steady-state level of 2.00 mg, while wing stiffness increased exponentially by 90.7% until it reached a steady-state level of 1.70 mN mm{sup -1}. (communication)

Mechanical characterization of journal superconducting magnetic bearings: stiffness, hysteresis and force relaxation

International Nuclear Information System (INIS)

Cristache, Cristian; Valiente-Blanco, Ignacio; Diez-Jimenez, Efren; Alvarez-Valenzuela, Marco Antonio; Perez-Diaz, Jose Luis; Pato, Nelson

2014-01-01

Superconducting magnetic bearings (SMBs) can provide stable levitation without direct contact between them and a magnetic source (typically a permanent magnet). In this context, superconducting magnetic levitation provides a new tool for mechanical engineers to design non-contact mechanisms solving the tribological problems associated with contact at very low temperatures. In the last years, different mechanisms have been proposed taking advantage of superconducting magnetic levitation. Flywheels, conveyors or mechanisms for high-precision positioning. In this work the mechanical stiffness of a journal SMBs have been experimentally studied. Both radial and axial stiffness have been considered. The influence of the size and shape of the permanent magnets (PM), the size and shape of the HTS, the polarization and poles configuration of PMs of the journal SMB have been studied experimentally. Additionally, in this work hysteresis behavior and force relaxation are considered because they are essential for mechanical engineer when designing bearings that hold levitating axles.

Solving applied mathematical problems with Matlab

CERN Document Server

Xue, Dingyu

2008-01-01

Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.

Differential equation analysis in biomedical science and engineering ordinary differential equation applications with R

CERN Document Server

Schiesser, William E

2014-01-01

Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-worldODE problems that are found in a variety of fields, including chemistry, physics, biology,and physiology. The book provides readers with the necessary knowledge to reproduce andextend the comp

Shoulder Stiffness : Current Concepts and Concerns

NARCIS (Netherlands)

Itoi, Eiji; Arce, Guillermo; Bain, Gregory I.; Diercks, Ronald L.; Guttmann, Dan; Imhoff, Andreas B.; Mazzocca, Augustus D.; Sugaya, Hiroyuki; Yoo, Yon-Sik

Shoulder stiffness can be caused by various etiologies such as immobilization, trauma, or surgical interventions. The Upper Extremity Committee of ISAKOS defined the term "frozen shoulder" as idiopathic stiff shoulder, that is, without a known cause. Secondary stiff shoulder is a term that should be

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

Science.gov (United States)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

The link between exercise and titin passive stiffness.

Science.gov (United States)

Lalande, Sophie; Mueller, Patrick J; Chung, Charles S

2017-09-01

What is the topic of this review? This review focuses on how in vivo and molecular measurements of cardiac passive stiffness can predict exercise tolerance and how exercise training can reduce cardiac passive stiffness. What advances does it highlight? This review highlights advances in understanding the relationship between molecular (titin-based) and in vivo (left ventricular) passive stiffness, how passive stiffness modifies exercise tolerance, and how exercise training may be therapeutic for cardiac diseases with increased passive stiffness. Exercise can help alleviate the negative effects of cardiovascular disease and cardiovascular co-morbidities associated with sedentary behaviour; this may be especially true in diseases that are associated with increased left ventricular passive stiffness. In this review, we discuss the inverse relationship between exercise tolerance and cardiac passive stiffness. Passive stiffness is the physical property of cardiac muscle to produce a resistive force when stretched, which, in vivo, is measured using the left ventricular end diastolic pressure-volume relationship or is estimated using echocardiography. The giant elastic protein titin is the major contributor to passive stiffness at physiological muscle (sarcomere) lengths. Passive stiffness can be modified by altering titin isoform size or by post-translational modifications. In both human and animal models, increased left ventricular passive stiffness is associated with reduced exercise tolerance due to impaired diastolic filling, suggesting that increased passive stiffness predicts reduced exercise tolerance. At the same time, exercise training itself may induce both short- and long-term changes in titin-based passive stiffness, suggesting that exercise may be a treatment for diseases associated with increased passive stiffness. Direct modification of passive stiffness to improve exercise tolerance is a potential therapeutic approach. Titin passive stiffness itself may

Differential equation analysis in biomedical science and engineering partial differential equation applications with R

CERN Document Server

Schiesser, William E

2014-01-01

Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the com

Efficient Method for Calculating the Composite Stiffness of Parabolic Leaf Springs with Variable Stiffness for Vehicle Rear Suspension

Directory of Open Access Journals (Sweden)

Wen-ku Shi

2016-01-01

Full Text Available The composite stiffness of parabolic leaf springs with variable stiffness is difficult to calculate using traditional integral equations. Numerical integration or FEA may be used but will require computer-aided software and long calculation times. An efficient method for calculating the composite stiffness of parabolic leaf springs with variable stiffness is developed and evaluated to reduce the complexity of calculation and shorten the calculation time. A simplified model for double-leaf springs with variable stiffness is built, and a composite stiffness calculation method for the model is derived using displacement superposition and material deformation continuity. The proposed method can be applied on triple-leaf and multileaf springs. The accuracy of the calculation method is verified by the rig test and FEA analysis. Finally, several parameters that should be considered during the design process of springs are discussed. The rig test and FEA analytical results indicate that the calculated results are acceptable. The proposed method can provide guidance for the design and production of parabolic leaf springs with variable stiffness. The composite stiffness of the leaf spring can be calculated quickly and accurately when the basic parameters of the leaf spring are known.

Hydration Status Is Associated with Aortic Stiffness, but Not with Peripheral Arterial Stiffness, in Chronically Hemodialysed Patients

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Daniel Bia

2015-01-01

Full Text Available Background. Adequate fluid management could be essential to minimize high arterial stiffness observed in chronically hemodialyzed patients (CHP. Aim. To determine the association between body fluid status and central and peripheral arterial stiffness levels. Methods. Arterial stiffness was assessed in 65 CHP by measuring the pulse wave velocity (PWV in a central arterial pathway (carotid-femoral and in a peripheral pathway (carotid-brachial. A blood pressure-independent regional arterial stiffness index was calculated using PWV. Volume status was assessed by whole-body multiple-frequency bioimpedance. Patients were first observed as an entire group and then divided into three different fluid status-related groups: normal, overhydration, and dehydration groups. Results. Only carotid-femoral stiffness was positively associated (P<0.05 with the hydration status evaluated through extracellular/intracellular fluid, extracellular/Total Body Fluid, and absolute and relative overhydration. Conclusion. Volume status and overload are associated with central, but not peripheral, arterial stiffness levels with independence of the blood pressure level, in CHP.

Arterial stiffness, central hemodynamics, and cardiovascular risk in hypertension

Science.gov (United States)

Palatini, Paolo; Casiglia, Edoardo; Gąsowski, Jerzy; Głuszek, Jerzy; Jankowski, Piotr; Narkiewicz, Krzysztof; Saladini, Francesca; Stolarz-Skrzypek, Katarzyna; Tikhonoff, Valérie; Van Bortel, Luc; Wojciechowska, Wiktoria; Kawecka-Jaszcz, Kalina

2011-01-01

This review summarizes several scientific contributions at the recent Satellite Symposium of the European Society of Hypertension, held in Milan, Italy. Arterial stiffening and its hemodynamic consequences can be easily and reliably measured using a range of noninvasive techniques. However, like blood pressure (BP) measurements, arterial stiffness should be measured carefully under standardized patient conditions. Carotid-femoral pulse wave velocity has been proposed as the gold standard for arterial stiffness measurement and is a well recognized predictor of adverse cardiovascular outcome. Systolic BP and pulse pressure in the ascending aorta may be lower than pressures measured in the upper limb, especially in young individuals. A number of studies suggest closer correlation of end-organ damage with central BP than with peripheral BP, and central BP may provide additional prognostic information regarding cardiovascular risk. Moreover, BP-lowering drugs can have differential effects on central aortic pressures and hemodynamics compared with brachial BP. This may explain the greater beneficial effect provided by newer antihypertensive drugs beyond peripheral BP reduction. Although many methodological problems still hinder the wide clinical application of parameters of arterial stiffness, these will likely contribute to cardiovascular assessment and management in future clinical practice. Each of the abovementioned parameters reflects a different characteristic of the atherosclerotic process, involving functional and/or morphological changes in the vessel wall. Therefore, acquiring simultaneous measurements of different parameters of vascular function and structure could theoretically enhance the power to improve risk stratification. Continuous technological effort is necessary to refine our methods of investigation in order to detect early arterial abnormalities. Arterial stiffness and its consequences represent the great challenge of the twenty-first century for

Physically Inspired Models for the Synthesis of Stiff Strings with Dispersive Waveguides

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Testa I

2004-01-01

Full Text Available We review the derivation and design of digital waveguides from physical models of stiff systems, useful for the synthesis of sounds from strings, rods, and similar objects. A transform method approach is proposed to solve the classic fourth-order equations of stiff systems in order to reduce it to two second-order equations. By introducing scattering boundary matrices, the eigenfrequencies are determined and their dependency is discussed for the clamped, hinged, and intermediate cases. On the basis of the frequency-domain physical model, the numerical discretization is carried out, showing how the insertion of an all-pass delay line generalizes the Karplus-Strong algorithm for the synthesis of ideally flexible vibrating strings. Knowing the physical parameters, the synthesis can proceed using the generalized structure. Another point of view is offered by Laguerre expansions and frequency warping, which are introduced in order to show that a stiff system can be treated as a nonstiff one, provided that the solutions are warped. A method to compute the all-pass chain coefficients and the optimum warping curves from sound samples is discussed. Once the optimum warping characteristic is found, the length of the dispersive delay line to be employed in the simulation is simply determined from the requirement of matching the desired fundamental frequency. The regularization of the dispersion curves by means of optimum unwarping is experimentally evaluated.

Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems

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Emran Tohidi

2013-01-01

Full Text Available The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.

Numerical analysis of systems of ordinary and stochastic differential equations

CERN Document Server

Artemiev, S S

1997-01-01

This text deals with numerical analysis of systems of both ordinary and stochastic differential equations. It covers numerical solution problems of the Cauchy problem for stiff ordinary differential equations (ODE) systems by Rosenbrock-type methods (RTMs).

Modeling Blazar Spectra by Solving an Electron Transport Equation

Science.gov (United States)

Lewis, Tiffany; Finke, Justin; Becker, Peter A.

2018-01-01

Blazars are luminous active galaxies across the entire electromagnetic spectrum, but the spectral formation mechanisms, especially the particle acceleration, in these sources are not well understood. We develop a new theoretical model for simulating blazar spectra using a self-consistent electron number distribution. Specifically, we solve the particle transport equation considering shock acceleration, adiabatic expansion, stochastic acceleration due to MHD waves, Bohm diffusive particle escape, synchrotron radiation, and Compton radiation, where we implement the full Compton cross-section for seed photons from the accretion disk, the dust torus, and 26 individual broad lines. We used a modified Runge-Kutta method to solve the 2nd order equation, including development of a new mathematical method for normalizing stiff steady-state ordinary differential equations. We show that our self-consistent, transport-based blazar model can qualitatively fit the IR through Fermi g-ray data for 3C 279, with a single-zone, leptonic configuration. We use the solution for the electron distribution to calculate multi-wavelength SED spectra for 3C 279. We calculate the particle and magnetic field energy densities, which suggest that the emitting region is not always in equipartition (a common assumption), but sometimes matter dominated. The stratified broad line region (based on ratios in quasar reverberation mapping, and thus adding no free parameters) improves our estimate of the location of the emitting region, increasing it by ~5x. Our model provides a novel view into the physics at play in blazar jets, especially the relative strength of the shock and stochastic acceleration, where our model is well suited to distinguish between these processes, and we find that the latter tends to dominate.

Differentiation of benign and malignant solid pancreatic masses using magnetic resonance elastography with spin-echo echo planar imaging and three-dimensional inversion reconstruction. A prospective study

Energy Technology Data Exchange (ETDEWEB)

Shi, Yu; Yu, Bing; Liu, Yanqing; Guo, Qiyong [Shengjing Hospital of China Medical University, Department of Radiology, Shenyang (China); Gao, Feng [Shengjing Hospital of China Medical University, Department of Hepato-Pancreato-Biliary Tumour Surgery, Shenyang (China); Li, Yue [Shengjing Hospital of China Medical University, Department of Pathology, Shenyang (China); Tao, Shengzhen; Glaser, Kevin J.; Ehman, Richard L. [Mayo Clinic, Department of Radiology, Rochester, MN (United States); Liu, Zaiyi [Guangdong Academy of Medical Sciences, Department of Radiology, Guangdong General Hospital, Guangdong (China)

2018-03-15

To determine the diagnostic performance of MR elastography (MRE) and compare it with serum CA19-9 in differentiating malignant from benign pancreatic masses, with emphasis on differentiating between pancreatic ductal adenocarcinoma (PDAC) and mass-forming pancreatitis (MFP). We performed a prospective, consecutive, 24-month study in 85 patients with solid pancreatic masses confirmed by histopathologic examinations. The mass stiffness and stiffness ratio (calculated as the ratio of mass stiffness to the parenchymal stiffness) were assessed. The diagnostic accuracy was analysed by calculating the area under the ROC curve (AUROC). The final diagnosis included 54 malignant tumours (43 patients with PDAC) and 31 benign masses (24 patients with MFP). The stiffness ratio showed better diagnostic performance than the mass stiffness and serum CA19-9 for the differentiation between malignant and benign masses (AUC: 0.912 vs. 0.845 vs. 0.702; P = 0.026, P < 0.001) and, specifically, between PDAC and MFP (AUC: 0.955 vs. 0.882 vs. 0.745; P = 0.026, P = 0.003). The sensitivity, specificity, and accuracy of stiffness ratio for the differentiation of PDAC and MFP were all higher than 0.9. MRE presents an effective and quantitative strategy for non-invasive differentiation between PDAC and MFP based on their mechanical properties. (orig.)

Factors influencing the stiffness of fibroadenomas at shear wave elastography

International Nuclear Information System (INIS)

Elseedawy, M.; Whelehan, P.; Vinnicombe, S.; Thomson, K.; Evans, A.

2016-01-01

Aim: To identify which features of fibroadenomas are associated with false-positive findings at shear wave elastography (SWE). Materials and methods: A total of 151 patients with histologically confirmed fibroadenomata were identified from a prospective database, from a single breast unit. The following features were assessed by two observers who were unaware of the SWE findings: patient age, grey-scale ultrasound lesion diameter (<15 or ≥15 mm), distance from the lesion to skin, composition of surrounding tissue (fatty, mixed or dense), and source of referral (screening or symptomatic). Statistical analysis was carried out using the chi-square test. Results: A statistically significant positive association was found between grey-scale ultrasound lesion size and lesion stiffness. Twenty-nine of 70 (41%) lesions ≥15 mm were stiff, versus 10 of 81 (12%) <15 mm (p=0.001). Patient age, distance from the lesion to skin, make-up of surrounding tissue, and source were not significantly associated with stiffness. Conclusion: Fibroadenomas giving false-positive SWE results tend to be larger in size than those that do not. More compression of adjacent normal tissue is assumed to be the cause of the present findings. As previous studies have shown that large cancers tend to be stiffer than smaller cancers, it may be appropriate to vary the quantitative cut-off value used for benign/malignant differentiation in SWE according to lesion size. - Highlights: • Fibroadenomas giving false positive SWE results tend to be larger in size. • More compression of adjacent normal tissue is assumed to be the cause of our findings. • The age of the patient is not related to fibroadenoma stiffness.

Solution of initial value problems using ndsolve of mathematica ...

African Journals Online (AJOL)

In the paper, the hyperbolic equations of the form (1) are approximated by the semi-finite difference schemes O(h2) and O(h4) accurate. The resulting two stiff systems of ordinary differential equations with initial conditions are solved by a Mathematica modules utilizing the function NDSolve. The stiffness ratios of the ...

Stretching human mesenchymal stromal cells on stiffness-customized collagen type I generates a smooth muscle marker profile without growth factor addition

Science.gov (United States)

Rothdiener, Miriam; Hegemann, Miriam; Uynuk-Ool, Tatiana; Walters, Brandan; Papugy, Piruntha; Nguyen, Phong; Claus, Valentin; Seeger, Tanja; Stoeckle, Ulrich; Boehme, Karen A.; Aicher, Wilhelm K.; Stegemann, Jan P.; Hart, Melanie L.; Kurz, Bodo; Klein, Gerd; Rolauffs, Bernd

2016-10-01

Using matrix elasticity and cyclic stretch have been investigated for inducing mesenchymal stromal cell (MSC) differentiation towards the smooth muscle cell (SMC) lineage but not in combination. We hypothesized that combining lineage-specific stiffness with cyclic stretch would result in a significantly increased expression of SMC markers, compared to non-stretched controls. First, we generated dense collagen type I sheets by mechanically compressing collagen hydrogels. Atomic force microscopy revealed a nanoscale stiffness range known to support myogenic differentiation. Further characterization revealed viscoelasticity and stable biomechanical properties under cyclic stretch with >99% viable adherent human MSC. MSCs on collagen sheets demonstrated a significantly increased mRNA but not protein expression of SMC markers, compared to on culture flasks. However, cyclic stretch of MSCs on collagen sheets significantly increased both mRNA and protein expression of α-smooth muscle actin, transgelin, and calponin versus plastic and non-stretched sheets. Thus, lineage-specific stiffness and cyclic stretch can be applied together for inducing MSC differentiation towards SMCs without the addition of recombinant growth factors or other soluble factors. This represents a novel stimulation method for modulating the phenotype of MSCs towards SMCs that could easily be incorporated into currently available methodologies to obtain a more targeted control of MSC phenotype.

Real-Time Vision-Based Stiffness Mapping †.

Science.gov (United States)

Faragasso, Angela; Bimbo, João; Stilli, Agostino; Wurdemann, Helge Arne; Althoefer, Kaspar; Asama, Hajime

2018-04-26

This paper presents new findings concerning a hand-held stiffness probe for the medical diagnosis of abnormalities during palpation of soft-tissue. Palpation is recognized by the medical community as an essential and low-cost method to detect and diagnose disease in soft-tissue. However, differences are often subtle and clinicians need to train for many years before they can conduct a reliable diagnosis. The probe presented here fills this gap providing a means to easily obtain stiffness values of soft tissue during a palpation procedure. Our stiffness sensor is equipped with a multi degree of freedom (DoF) Aurora magnetic tracker, allowing us to track and record the 3D position of the probe whilst examining a tissue area, and generate a 3D stiffness map in real-time. The stiffness probe was integrated in a robotic arm and tested in an artificial environment representing a good model of soft tissue organs; the results show that the sensor can accurately measure and map the stiffness of a silicon phantom embedded with areas of varying stiffness.

Real-Time Vision-Based Stiffness Mapping †

Directory of Open Access Journals (Sweden)

Angela Faragasso

2018-04-01

Full Text Available This paper presents new findings concerning a hand-held stiffness probe for the medical diagnosis of abnormalities during palpation of soft-tissue. Palpation is recognized by the medical community as an essential and low-cost method to detect and diagnose disease in soft-tissue. However, differences are often subtle and clinicians need to train for many years before they can conduct a reliable diagnosis. The probe presented here fills this gap providing a means to easily obtain stiffness values of soft tissue during a palpation procedure. Our stiffness sensor is equipped with a multi degree of freedom (DoF Aurora magnetic tracker, allowing us to track and record the 3D position of the probe whilst examining a tissue area, and generate a 3D stiffness map in real-time. The stiffness probe was integrated in a robotic arm and tested in an artificial environment representing a good model of soft tissue organs; the results show that the sensor can accurately measure and map the stiffness of a silicon phantom embedded with areas of varying stiffness.

Dynamic stiffness of suction caissons - vertical vibrations

Energy Technology Data Exchange (ETDEWEB)

Ibsen, Lars Bo; Liingaard, M.; Andersen, Lars

2006-12-15

The dynamic response of offshore wind turbines are affected by the properties of the foundation and the subsoil. The purpose of this report is to evaluate the dynamic soil-structure interaction of suction caissons for offshore wind turbines. The investigation is limited to a determination of the vertical dynamic stiffness of suction caissons. The soil surrounding the foundation is homogenous with linear viscoelastic properties. The dynamic stiffness of the suction caisson is expressed by dimensionless frequency-dependent dynamic stiffness coefficients corresponding to the vertical degree of freedom. The dynamic stiffness coefficients for the foundations are evaluated by means of a dynamic three-dimensional coupled Boundary Element/Finite Element model. Comparisons are made with known analytical and numerical solutions in order to evaluate the static and dynamic behaviour of the Boundary Element/Finite Element model. The vertical frequency dependent stiffness has been determined for different combinations of the skirt length, Poisson's ratio and the ratio between soil stiffness and skirt stiffness. Finally the dynamic behaviour at high frequencies is investigated. (au)

Observer-Based Human Knee Stiffness Estimation.

Science.gov (United States)

Misgeld, Berno J E; Luken, Markus; Riener, Robert; Leonhardt, Steffen

2017-05-01

We consider the problem of stiffness estimation for the human knee joint during motion in the sagittal plane. The new stiffness estimator uses a nonlinear reduced-order biomechanical model and a body sensor network (BSN). The developed model is based on a two-dimensional knee kinematics approach to calculate the angle-dependent lever arms and the torques of the muscle-tendon-complex. To minimize errors in the knee stiffness estimation procedure that result from model uncertainties, a nonlinear observer is developed. The observer uses the electromyogram (EMG) of involved muscles as input signals and the segmental orientation as the output signal to correct the observer-internal states. Because of dominating model nonlinearities and nonsmoothness of the corresponding nonlinear functions, an unscented Kalman filter is designed to compute and update the observer feedback (Kalman) gain matrix. The observer-based stiffness estimation algorithm is subsequently evaluated in simulations and in a test bench, specifically designed to provide robotic movement support for the human knee joint. In silico and experimental validation underline the good performance of the knee stiffness estimation even in the cases of a knee stiffening due to antagonistic coactivation. We have shown the principle function of an observer-based approach to knee stiffness estimation that employs EMG signals and segmental orientation provided by our own IPANEMA BSN. The presented approach makes realtime, model-based estimation of knee stiffness with minimal instrumentation possible.

Give me a hand: Differential effects of gesture type in guiding young children's problem-solving

Science.gov (United States)

Vallotton, Claire; Fusaro, Maria; Hayden, Julia; Decker, Kalli; Gutowski, Elizabeth

2015-01-01

Adults’ gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents’ use of gestures to support their young children (1.5 – 6 years) in a block puzzle task (N = 126 parent-child dyads), and identified patterns in parents’ gesture use indicating different gestural strategies. Further, we examined the effect of child age on both the frequency and types of gestures parents used, and on their usefulness to support children's learning. Children attempted to solve the puzzle independently before and after receiving help from their parent; half of the parents were instructed to sit on their hands while they helped. Parents who could use their hands appear to use gestures in three strategies: orienting the child to the task, providing abstract information, and providing embodied information; further, they adapted their gesturing to their child's age and skill level. Younger children elicited more frequent and more proximal gestures from parents. Despite the greater use of gestures with younger children, it was the oldest group (4.5-6.0 years) who were most affected by parents’ gestures. The oldest group was positively affected by the total frequency of parents’ gestures, and in particular, parents’ use of embodying gestures (indexes that touched their referents, representational demonstrations with object in hand, and physically guiding child's hands). Though parents rarely used the embodying strategy with older children, it was this strategy which most enhanced the problem-solving of children 4.5 – 6 years. PMID:26848192

Give me a hand: Differential effects of gesture type in guiding young children's problem-solving.

Science.gov (United States)

Vallotton, Claire; Fusaro, Maria; Hayden, Julia; Decker, Kalli; Gutowski, Elizabeth

2015-11-01

Adults' gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents' use of gestures to support their young children (1.5 - 6 years) in a block puzzle task (N = 126 parent-child dyads), and identified patterns in parents' gesture use indicating different gestural strategies. Further, we examined the effect of child age on both the frequency and types of gestures parents used, and on their usefulness to support children's learning. Children attempted to solve the puzzle independently before and after receiving help from their parent; half of the parents were instructed to sit on their hands while they helped. Parents who could use their hands appear to use gestures in three strategies: orienting the child to the task, providing abstract information, and providing embodied information; further, they adapted their gesturing to their child's age and skill level. Younger children elicited more frequent and more proximal gestures from parents. Despite the greater use of gestures with younger children, it was the oldest group (4.5-6.0 years) who were most affected by parents' gestures. The oldest group was positively affected by the total frequency of parents' gestures, and in particular, parents' use of embodying gestures (indexes that touched their referents, representational demonstrations with object in hand, and physically guiding child's hands). Though parents rarely used the embodying strategy with older children, it was this strategy which most enhanced the problem-solving of children 4.5 - 6 years.

Optimization of a quasi-zero-stiffness isolator

International Nuclear Information System (INIS)

Carrella, A.; Brennan, M. J.; Waters, T. P.

2007-01-01

The frequency range over which a mount can isolate a mass from a vibrating base (or vice versa) is often limited by the mount stiffness required to support the weight of the mass. This compromise can be made more favourable by employing non-linear mounts with a softening spring characteristic such that small excursions about the static equilibrium position result in small dynamic spring forces and a correspondingly low natural frequency. This paper concerns the force-displacement characteristic of a so-called quasi-zero-stiffness (QZS) mechanism which is characterised by an appreciable static stiffness but very small (theoretically zero) dynamic stiffness. The mechanism studied comprises a vertical spring acting in parallel with two further springs which, when inclined at an appropriate angle to the vertical, produce a cancelling negative stiffness effect. Analysis of the system shows that a QZS characteristic can be obtained if the systems parameters (angle of inclination and ratio of spring stiffness) are opportunely chosen. By introducing the additional criterion that the displacement of the system be largest without exceeding a desired (low) value of stiffness an optimal set of parameter values is derived. Under sufficiently large displacements the stiffness of the QZS mechanism can eventually exceed that of the simple mass-spring system and criteria for this detrimental scenario to arise are presented

Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm

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F. F. Ngwane

2015-01-01

Full Text Available We propose a block hybrid trigonometrically fitted (BHT method, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs, including systems arising from the semidiscretization of hyperbolic Partial Differential Equations (PDEs, such as the Telegraph equation. The BHT is formulated from eight discrete hybrid formulas which are provided by a continuous two-step hybrid trigonometrically fitted method with two off-grid points. The BHT is implemented in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHT is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.

Measuring the correlation between cell mechanics and myofibroblastic differentiation during maturation of 3D microtissues

Science.gov (United States)

Zhao, Ruogang; Wang, Weigang; Boudou, Thomas; Chen, Christopher; Reich, Daniel

2013-03-01

Tissue stiffness and cellular contractility are two of the most important biomechanical factors regulating pathological transitions of encapsulated cells, such as the differentiation of fibroblasts into myofibroblasts - a key event contributing to tissue fibrosis. However, a quantitative correlation between tissue stiffness and cellular contraction and myofibroblast differentiation has not yet been established in 3D environments, mainly due to the lack of suitable 3D tissue culture models that allow both tissue remodeling and simultaneous measurement of the cell/tissue mechanics. To address this, we have developed a magnetic microtissue tester system that allows the remodeling of arrays of cell-laden 3D collagen microtissues and the measurement of cell and tissue mechanics using magnetically actuated elastomeric microcantilevers. By measuring the development of cell/tissue mechanical properties and the expression level of α-smooth muscle actin (α-SMA, a marker for myofibroblast differentiation) during a 6 day culture period, we found microtissue stiffness increased by 45% and α-SMA expression increased by 38%, but tissue contraction forces only increased by 10%, indicating that tissue stiffness may be the predominant mechanical factor for regulation of myofibroblast differentiation. This study provides new quantitative insight into the regulatory effect of cell and tissue mechanics on cellular function. Supported in part by NIH grant HL090747

Explicit appropriate basis function method for numerical solution of stiff systems

International Nuclear Information System (INIS)

Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling

2015-01-01

Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations

Constitutive Modelling of Resins in the Stiffness Domain

Science.gov (United States)

Klasztorny, M.

2004-09-01

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic. The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.

Modulation of Huh7.5 spheroid formation and functionality using modified PEG-based hydrogels of different stiffness.

Directory of Open Access Journals (Sweden)

Bae Hoon Lee

Full Text Available Physical cues, such as cell microenvironment stiffness, are known to be important factors in modulating cellular behaviors such as differentiation, viability, and proliferation. Apart from being able to trigger these effects, mechanical stiffness tuning is a very convenient approach that could be implemented readily into smart scaffold designs. In this study, fibrinogen-modified poly(ethylene glycol-diacrylate (PEG-DA based hydrogels with tunable mechanical properties were synthesized and applied to control the spheroid formation and liver-like function of encapsulated Huh7.5 cells in an engineered, three-dimensional liver tissue model. By controlling hydrogel stiffness (0.1-6 kPa as a cue for mechanotransduction representing different stiffness of a normal liver and a diseased cirrhotic liver, spheroids ranging from 50 to 200 μm were formed over a three week time-span. Hydrogels with better compliance (i.e. lower stiffness promoted formation of larger spheroids. The highest rates of cell proliferation, albumin secretion, and CYP450 expression were all observed for spheroids in less stiff hydrogels like a normal liver in a healthy state. We also identified that the hydrogel modification by incorporation of PEGylated-fibrinogen within the hydrogel matrix enhanced cell survival and functionality possibly owing to more binding of autocrine fibronectin. Taken together, our findings establish guidelines to control the formation of Huh7.5 cell spheroids in modified PEGDA based hydrogels. These spheroids may serve as models for applications such as screening of pharmacological drug candidates.

New method for solving three-dimensional Schroedinger equation

International Nuclear Information System (INIS)

Melezhik, V.S.

1992-01-01

A new method is developed for solving the multidimensional Schroedinger equation without the variable separation. To solve the Schroedinger equation in a multidimensional coordinate space X, a difference grid Ω i (i=1,2,...,N) for some of variables, Ω, from X={R,Ω} is introduced and the initial partial-differential equation is reduced to a system of N differential-difference equations in terms of one of the variables R. The arising multi-channel scattering (or eigenvalue) problem is solved by the algorithm based on a continuous analog of the Newton method. The approach has been successfully tested for several two-dimensional problems (scattering on a nonspherical potential well and 'dipole' scatterer, a hydrogen atom in a homogenous magnetic field) and for a three-dimensional problem of the helium-atom bound states. (author)

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

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Jieyu Ding

2014-01-01

Full Text Available Nonlinear equilibrium curvatures and free vibration characteristics of a two-pulley belt-driven system with belt bending stiffness and a one-way clutch are investigated. With nonlinear dynamical tension, the transverse vibrations of the translating belt spans and the rotation motions of the pulleys and the accessory shaft are coupled. Therefore, nonlinear piecewise discrete-continuous governing equations are established. Considering the bending stiffness of the translating belt spans, the belt spans are modeled as axially moving beams. The pattern of equilibria is a nontrivial solution. Furthermore, the nontrivial equilibriums of the dynamical system are numerically determined by using two different approaches. The governing equations of the vibration near the equilibrium solutions are derived by introducing a coordinate transform. The natural frequencies of the dynamical systems are studied by using the Galerkin method with various truncations and the differential and integral quadrature methods. Moreover, the convergence of the Galerkin truncation is investigated. Numerical results reveal that the study needs 16 terms after truncation in order to determine the free vibration characteristics of the pulley-belt system with the belt bending stiffness. Furthermore, the first five natural frequencies are very sensitive to the bending stiffness of the translating belt.

The stiffness change and the increase in the ultimate capacity for a stiff pile resulting from a cyclic loading

DEFF Research Database (Denmark)

Lada, Aleksandra; Ibsen, Lars Bo; Nicolai, Giulio

In the paper the experimental results of small-scale tests on a stiff monopile are presented to outline the change in stiffness during the cyclic loading and the change in the ultimate pile capacity. The results confirm the increase of stiffness and the increase in bearing capacity resulting from...

Analytical study of a quasi-zero stiffness coupling using a torsion magnetic spring with negative stiffness

Science.gov (United States)

Zheng, Yisheng; Zhang, Xinong; Luo, Yajun; Zhang, Yahong; Xie, Shilin

2018-02-01

By now, many translation quasi-zero stiffness (QZS) mechanisms have been proposed to overcome the restriction between the isolation frequency range and the load bearing capacity of linear isolators. The couplings of rotor systems undertake the functions of transmitting static driving torque and isolating disturbing torque simultaneously, which creates the demand of torsion QZS mechanisms. Hence a QZS coupling is presented in this paper, where a torsion magnetic spring (TMS) composed of two coaxial ring magnet arrangements in repulsive configuration is employed to produce negative torsion stiffness to counteract the positive stiffness of a rubber spring. In this paper, the expressions of magnetic torque and stiffness are given firstly and verified by finite element simulations; and the effect of geometric parameters of the TMS on its stiffness characteristic is analyzed in detail, which contributes to the optimal design of the TMS. Then dynamic analysis of the QZS coupling is performed and the analytical expression of the torque transmissibility is achieved based on the Harmonic Balance Method. Finally, simulation of the torque transmissibility is carried out to reveal how geometric parameters of the TMS affect the isolation performance.

Differential equations for dummies

CERN Document Server

Holzner, Steven

2008-01-01

The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

Stiffness of Railway Soil-Steel Structures

Directory of Open Access Journals (Sweden)

Machelski Czesław

2015-12-01

Full Text Available The considerable influence of the soil backfill properties and that of the method of compacting it on the stiffness of soil-steel structures is characteristic of the latter. The above factors (exhibiting randomness become apparent in shell deformation measurements conducted during construction and proof test loading. A definition of soil-shell structure stiffness, calculated on the basis of shell deflection under the service load, is proposed in the paper. It is demonstrated that the stiffness is the inverse of the deflection influence function used in structural mechanics. The moving load methodology is shown to be useful for testing, since it makes it possible to map the shell deflection influence line also in the case of group loads (concentrated forces, as in bridges. The analyzed cases show that the shell’s span, geometry (static scheme and the height of earth fill influence the stiffness of the structure. The soil-steel structure’s characteristic parameter in the form of stiffness k is more suitable for assessing the quality of construction works than the proposed in code geometric index ω applied to beam structures. As shown in the given examples, parameter k is more effective than stiffness parameter λ used to estimate the deformation of soil-steel structures under construction. Although the examples concern railway structures, the methodology proposed in the paper is suitable also for road bridges.

Stiffness of Railway Soil-Steel Structures

Science.gov (United States)

Machelski, Czesław

2015-12-01

The considerable influence of the soil backfill properties and that of the method of compacting it on the stiffness of soil-steel structures is characteristic of the latter. The above factors (exhibiting randomness) become apparent in shell deformation measurements conducted during construction and proof test loading. A definition of soil-shell structure stiffness, calculated on the basis of shell deflection under the service load, is proposed in the paper. It is demonstrated that the stiffness is the inverse of the deflection influence function used in structural mechanics. The moving load methodology is shown to be useful for testing, since it makes it possible to map the shell deflection influence line also in the case of group loads (concentrated forces), as in bridges. The analyzed cases show that the shell's span, geometry (static scheme) and the height of earth fill influence the stiffness of the structure. The soil-steel structure's characteristic parameter in the form of stiffness k is more suitable for assessing the quality of construction works than the proposed in code geometric index ω applied to beam structures. As shown in the given examples, parameter k is more effective than stiffness parameter λ used to estimate the deformation of soil-steel structures under construction. Although the examples concern railway structures, the methodology proposed in the paper is suitable also for road bridges.

On matrix fractional differential equations

Directory of Open Access Journals (Sweden)

Adem Kılıçman

2017-01-01

Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

Matrix stiffness and oxigen tension modulate epigenetic conversion of mouse dermal fibroblasts into insulin producing cells.

Directory of Open Access Journals (Sweden)

Alessandro Zenobi

2017-05-01

Full Text Available In vivo, cells are surrounded by a three-dimensional (3-D organization of supporting matrix, neighboring cells and a gradient of chemical and mechanical signals (Antoni, et al., 2015. However, the present understanding of many biological processes is mainly based on two-dimensional (2-D systems that typically provides a static environment. In the present study, we tested two different 3-D culture systems and apply them to the epigenetic conversion of mouse dermal fibroblasts into insulin producing-cells (Pennarossa, et al., 2013; Brevini, et al., 2015, combining also the use of two oxygen tensions. In particular, cells were differentiated using the Polytetrafluoroethylene micro-bioreactor (PTFE and the Polyacrylamide (PAA gels with different stiffness (1 kPa; 4 kPa, maintained either in the standard 20% or in the more physiological 5% oxygen tensions. Standard differentiation performed on plastic substrates was assessed as a control. Cell morphology (Fig.1A, insulin expression and release were analyzed to evaluate the role of both stiffness and oxygen tension in the process. The results obtained showed that 1 kPa PAA gel and PTFE system induced a significantly higher insulin expression and release than plastic and 4 kPa PAA gel, especially in low oxygen condition (Fig.1B. Furthermore, comparing the efficiency of the two systems tested, 1 kPa PAA gel ensured a higher insulin transcription than PTFE (Fig.1C. Recent studies show the direct influence of substrates on lineage commitment and cell differentiation (Engler, et al., 2006; Evans, et al., 2009. The evidence here presented confirm that the use of an appropriate stiffness (similar to the pancreatic tissue, combined with a physiological oxygen tension, promote β-cell differentiation, with beneficial effects on cell functional activity and insulin release. The present results highlight the importance of 3-D cell rearrangement and oxigen tension to promote in vitro epigenetic conversion of

Solution of the reactor point kinetics equations by MATLAB computing

Directory of Open Access Journals (Sweden)

Singh Sudhansu S.

2015-01-01

Full Text Available The numerical solution of the point kinetics equations in the presence of Newtonian temperature feedback has been a challenging issue for analyzing the reactor transients. Reactor point kinetics equations are a system of stiff ordinary differential equations which need special numerical treatments. Although a plethora of numerical intricacies have been introduced to solve the point kinetics equations over the years, some of the simple and straightforward methods still work very efficiently with extraordinary accuracy. As an example, it has been shown recently that the fundamental backward Euler finite difference algorithm with its simplicity has proven to be one of the most effective legacy methods. Complementing the back-ward Euler finite difference scheme, the present work demonstrates the application of ordinary differential equation suite available in the MATLAB software package to solve the stiff reactor point kinetics equations with Newtonian temperature feedback effects very effectively by analyzing various classic benchmark cases. Fair accuracy of the results implies the efficient application of MATLAB ordinary differential equation suite for solving the reactor point kinetics equations as an alternate method for future applications.

Discrete computational mechanics for stiff phenomena

KAUST Repository

Michels, Dominik L.

2016-11-28

Many natural phenomena which occur in the realm of visual computing and computational physics, like the dynamics of cloth, fibers, fluids, and solids as well as collision scenarios are described by stiff Hamiltonian equations of motion, i.e. differential equations whose solution spectra simultaneously contain extremely high and low frequencies. This usually impedes the development of physically accurate and at the same time efficient integration algorithms. We present a straightforward computationally oriented introduction to advanced concepts from classical mechanics. We provide an easy to understand step-by-step introduction from variational principles over the Euler-Lagrange formalism and the Legendre transformation to Hamiltonian mechanics. Based on such solid theoretical foundations, we study the underlying geometric structure of Hamiltonian systems as well as their discrete counterparts in order to develop sophisticated structure preserving integration algorithms to efficiently perform high fidelity simulations.

Single motor–variable stiffness actuator using bistable switching mechanisms for independent motion and stiffness control

NARCIS (Netherlands)

Groothuis, Stefan; Carloni, Raffaella; Stramigioli, Stefano

This paper presents a proof of concept of a variable stiffness actuator (VSA) that uses only one (high power) input motor. In general, VSAs use two (high power) motors to be able to control both the output position and the output stiffness, which possibly results in a heavy, and bulky system. In

Big bang nucleosynthesis with a stiff fluid

International Nuclear Information System (INIS)

Dutta, Sourish; Scherrer, Robert J.

2010-01-01

Models that lead to a cosmological stiff fluid component, with a density ρ S that scales as a -6 , where a is the scale factor, have been proposed recently in a variety of contexts. We calculate numerically the effect of such a stiff fluid on the primordial element abundances. Because the stiff fluid energy density decreases with the scale factor more rapidly than radiation, it produces a relatively larger change in the primordial helium-4 abundance than in the other element abundances, relative to the changes produced by an additional radiation component. We show that the helium-4 abundance varies linearly with the density of the stiff fluid at a fixed fiducial temperature. Taking ρ S10 and ρ R10 to be the stiff fluid energy density and the standard density in relativistic particles, respectively, at T=10 MeV, we find that the change in the primordial helium abundance is well-fit by ΔY p =0.00024(ρ S10 /ρ R10 ). The changes in the helium-4 abundance produced by additional radiation or by a stiff fluid are identical when these two components have equal density at a 'pivot temperature', T * , where we find T * =0.55 MeV. Current estimates of the primordial 4 He abundance give the constraint on a stiff fluid energy density of ρ S10 /ρ R10 <30.

Direct measurement of the intrinsic ankle stiffness during standing.

Science.gov (United States)

Vlutters, M; Boonstra, T A; Schouten, A C; van der Kooij, H

2015-05-01

Ankle stiffness contributes to standing balance, counteracting the destabilizing effect of gravity. The ankle stiffness together with the compliance between the foot and the support surface make up the ankle-foot stiffness, which is relevant to quiet standing. The contribution of the intrinsic ankle-foot stiffness to balance, and the ankle-foot stiffness amplitude dependency remain a topic of debate in the literature. We therefore developed an experimental protocol to directly measure the bilateral intrinsic ankle-foot stiffness during standing balance, and determine its amplitude dependency. By applying fast (40 ms) ramp-and-hold support surface rotations (0.005-0.08 rad) during standing, reflexive contributions could be excluded, and the amplitude dependency of the intrinsic ankle-foot stiffness was investigated. Results showed that reflexive activity could not have biased the torque used for estimating the intrinsic stiffness. Furthermore, subjects required less recovery action to restore balance after bilateral rotations in opposite directions compared to rotations in the same direction. The intrinsic ankle-foot stiffness appears insufficient to ensure balance, ranging from 0.93±0.09 to 0.44±0.06 (normalized to critical stiffness 'mgh'). This implies that changes in muscle activation are required to maintain balance. The non-linear stiffness decrease with increasing rotation amplitude supports the previous published research. With the proposed method reflexive effects can be ruled out from the measured torque without any model assumptions, allowing direct estimation of intrinsic stiffness during standing. Copyright © 2015 Elsevier Ltd. All rights reserved.

Domain decomposition methods for solving an image problem

Energy Technology Data Exchange (ETDEWEB)

Tsui, W.K.; Tong, C.S. [Hong Kong Baptist College (Hong Kong)

1994-12-31

The domain decomposition method is a technique to break up a problem so that ensuing sub-problems can be solved on a parallel computer. In order to improve the convergence rate of the capacitance systems, pre-conditioned conjugate gradient methods are commonly used. In the last decade, most of the efficient preconditioners are based on elliptic partial differential equations which are particularly useful for solving elliptic partial differential equations. In this paper, the authors apply the so called covering preconditioner, which is based on the information of the operator under investigation. Therefore, it is good for various kinds of applications, specifically, they shall apply the preconditioned domain decomposition method for solving an image restoration problem. The image restoration problem is to extract an original image which has been degraded by a known convolution process and additive Gaussian noise.

Second derivative parallel block backward differentiation type ...

African Journals Online (AJOL)

Second derivative parallel block backward differentiation type formulas for Stiff ODEs. ... Log in or Register to get access to full text downloads. ... and the methods are inherently parallel and can be distributed over parallel processors. They are ...

DDASAC, Double-Precision Differential or Algebraic Sensitivity Analysis

International Nuclear Information System (INIS)

Caracotsios, M.; Stewart, W.E.; Petzold, L.

1997-01-01

1 - Description of program or function: DDASAC solves nonlinear initial-value problems involving stiff implicit systems of ordinary differential and algebraic equations. Purely algebraic nonlinear systems can also be solved, given an initial guess within the region of attraction of a solution. Options include automatic reconciliation of inconsistent initial states and derivatives, automatic initial step selection, direct concurrent parametric sensitivity analysis, and stopping at a prescribed value of any user-defined functional of the current solution vector. Local error control (in the max-norm or the 2-norm) is provided for the state vector and can include the sensitivities on request. 2 - Method of solution: Reconciliation of initial conditions is done with a damped Newton algorithm adapted from Bain and Stewart (1991). Initial step selection is done by the first-order algorithm of Shampine (1987), extended here to differential-algebraic equation systems. The solution is continued with the DASSL predictor- corrector algorithm (Petzold 1983, Brenan et al. 1989) with the initial acceleration phase detected and with row scaling of the Jacobian added. The backward-difference formulas for the predictor and corrector are expressed in divide-difference form, and the fixed-leading-coefficient form of the corrector (Jackson and Sacks-Davis 1980, Brenan et al. 1989) is used. Weights for error tests are updated in each step with the user's tolerances at the predicted state. Sensitivity analysis is performed directly on the corrector equations as given by Catacotsios and Stewart (1985) and is extended here to the initialization when needed. 3 - Restrictions on the complexity of the problem: This algorithm, like DASSL, performs well on differential-algebraic systems of index 0 and 1 but not on higher-index systems; see Brenan et al. (1989). The user assigns the work array lengths and the output unit. The machine number range and precision are determined at run time by a

Observed variations of monopile foundation stiffness

DEFF Research Database (Denmark)

Kallehave, Dan; Thilsted, C.L.; Diaz, Alberto Troya

2015-01-01

full-scale measurements obtained from one offshore wind turbine structure located within Horns Reef II offshore wind farm. Data are presented for a 2.5 years period and covers normal operating conditions and one larger storm event. A reduction of the pile-soil stiffness was observed during the storm...... events, followed by a complete regain to a pre-storm level when the storm subsided. In additional, no long term variations of the pile-soil stiffness was observed. The wind turbine is located in dense to very dense sand deposits.......The soil-structure stiffness of monopile foundations for offshore wind turbines has a high impact on the fatigue loading during normal operating conditions. Thus, a robust design must consider the evolution of pile-soil stiffness over the lifetime of the wind farm. This paper present and discuss...

Stiff Hands

Science.gov (United States)

... All Topics A-Z Videos Infographics Symptom Picker Anatomy Bones Joints Muscles Nerves Vessels Tendons About Hand Surgery What is a Hand Surgeon? What is a Hand Therapist? Media Find a Hand Surgeon Home Anatomy Stiff Hands Email to a friend * required fields ...

Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

International Nuclear Information System (INIS)

Chen, Jin

2009-01-01

Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

A Stewart isolator with high-static-low-dynamic stiffness struts based on negative stiffness magnetic springs

Science.gov (United States)

Zheng, Yisheng; Li, Qingpin; Yan, Bo; Luo, Yajun; Zhang, Xinong

2018-05-01

In order to improve the isolation performance of passive Stewart platforms, the negative stiffness magnetic spring (NSMS) is employed to construct high static low dynamic stiffness (HSLDS) struts. With the NSMS, the resonance frequencies of the platform can be reduced effectively without deteriorating its load bearing capacity. The model of the Stewart isolation platform with HSLDS struts is presented and the stiffness characteristic of its struts is studied firstly. Then the nonlinear dynamic model of the platform including both geometry nonlinearity and stiffness nonlinearity is established; and its simplified dynamic model is derived under the condition of small vibration. The effect of nonlinearity on the isolation performance is also evaluated. Finally, a prototype is built and the isolation performance is tested. Both simulated and experimental results demonstrate that, by using the NSMS, the resonance frequencies of the Stewart isolator are reduced and the isolation performance in all six directions is improved: the isolation frequency band is increased and extended to a lower-frequency level.

Stiffness and frictional resistance of a superelastic nickel-titanium orthodontic wire with low-stress hysteresis.

Science.gov (United States)

Liaw, Yu-Cheng; Su, Yu-Yu M; Lai, Yu-Lin; Lee, Shyh-Yuan

2007-05-01

Stress-induced martensite formation with stress hysteresis that changes the elasticity and stiffness of nickel-titanium (Ni-Ti) wire influences the sliding mechanics of archwire-guided tooth movement. This in-vitro study investigated the frictional behavior of an improved superelastic Ni-Ti wire with low-stress hysteresis. Improved superelastic Ni-Ti alloy wires (L & H Titan, Tomy International, Tokyo, Japan) with low-stress hysteresis were examined by using 3-point bending and frictional resistance tests with a universal test machine at a constant temperature of 35 degrees C, and compared with the former conventional austenitic-active superelastic Ni-Ti wires (Sentalloy, Tomy International). Wire stiffness levels were derived from differentiation of the polynomial regression of the unloading curves, and values for kinetic friction were measured at constant bending deflection distances of 0, 2, 3, and 4 mm, respectively. Compared with conventional Sentalloy wires, the L & H Titan wire had a narrower stress hysteresis including a lower loading plateau and a higher unloading plateau. In addition, L & H Titan wires were less stiff than the Sentalloy wires during most unloading stages. Values of friction measured at deflections of 0, 2, and 3 mm were significantly (P Sentalloy wires at all bending deflections (P <.05). Stress-induced martensite formation significantly reduced the stiffness and thus could be beneficial to decrease the binding friction of superelastic Ni-Ti wires during sliding with large bending deflections. Austenitic-active alloy wires with low-stress hysteresis and lower stiffness and friction offer significant potential for further investigation.

Comparison of magnetic resonance elastography and diffusion-weighted imaging for differentiating benign and malignant liver lesions

Energy Technology Data Exchange (ETDEWEB)

Hennedige, Tiffany P.; Hallinan, James Thomas Patrick Decourcy; Teo, Lynette Li San [National University Hospital, National University Health System, Department of Diagnostic Imaging, Singapore (Singapore); Leung, Fiona P. [National University Hospital, National University Health System, Department of Diagnostic Imaging, Singapore (Singapore); South West Radiology, Liverpool, NSW (Australia); Iyer, Sridhar; Chang, Stephen; Madhavan, Krishna Kumar [National University Health System, Department of Surgery, Singapore (Singapore); Wang, Gang [National University Hospital, National University Health System, Department of Diagnostic Imaging, Singapore (Singapore); University of Calgary, Alberta (Canada); Wee, Aileen [National University Hospital, National University Health System, Department of Pathology, Singapore (Singapore); Venkatesh, Sudhakar K. [Mayo Clinic, Department of Radiology, Rochester, MN (United States)

2016-02-15

Comparison of magnetic resonance elastography (MRE) and diffusion-weighted imaging (DWI) for differentiating malignant and benign focal liver lesions (FLLs). Seventy-nine subjects with 124 FLLs (44 benign and 80 malignant) underwent both MRE and DWI. MRE was performed with a modified gradient-echo sequence and DWI with a free breathing technique (b = 0.500). Apparent diffusion coefficient (ADC) maps and stiffness maps were generated. FLL mean stiffness and ADC values were obtained by placing regions of interest over the FLLs on stiffness and ADC maps. The accuracy of MRE and DWI for differentiation of benign and malignant FLL was compared using receiver operating curve (ROC) analysis. There was a significant negative correlation between stiffness and ADC (r = -0.54, p < 0.0001) of FLLs. Malignant FLLs had significantly higher mean stiffness (7.9kPa vs. 3.1kPa, p < 0.001) and lower mean ADC (129 vs. 200 x 10{sup -3}mm{sup 2}/s, p < 0.001) than benign FLLs. The sensitivity/specificity/positive predictive value/negative predictive value for differentiating malignant from benign FLLs with MRE (cut-off, >4.54kPa) and DWI (cut-off, <151 x 10{sup -3}mm{sup 2}/s) were 96.3/95.5/97.5/93.3 % (p < 0.001) and 85/81.8/88.3/75 % (p < 0.001), respectively. ROC analysis showed significantly higher accuracy for MRE than DWI (0.986 vs. 0.82, p = 0.0016). MRE is significantly more accurate than DWI for differentiating benign and malignant FLLs. (orig.)

A differential transformation approach for solving functional differential equations with multiple delays

Science.gov (United States)

Rebenda, Josef; Šmarda, Zdeněk

2017-07-01

In the paper an efficient semi-analytical approach based on the method of steps and the differential transformation is proposed for numerical approximation of solutions of functional differential models of delayed and neutral type on a finite interval of arbitrary length, including models with several constant delays. Algorithms for both commensurate and non-commensurate delays are described, applications are shown in examples. Validity and efficiency of the presented algorithms is compared with the variational iteration method, the Adomian decomposition method and the polynomial least squares method numerically. Matlab package DDE23 is used to produce reference numerical values.

A novel energy-efficient rotational variable stiffness actuator

NARCIS (Netherlands)

Rao, S.; Carloni, Raffaella; Stramigioli, Stefano

This paper presents the working principle, the design and realization of a novel rotational variable stiffness actuator, whose stiffness can be varied independently of its output angular position. This actuator is energy-efficient, meaning that the stiffness of the actuator can be varied by keeping

Chaotification of Quasi-zero Stiffness System Via Direct Time-delay Feedback

Directory of Open Access Journals (Sweden)

Shuyong Liu

2013-03-01

Full Text Available This paper presents a chaotification method based on direct time-delay feedback control for a quasi-zero-stiffness isolation system. An analytical function of time-delay feedback control is derived based on differential-geometry control theory. Furthermore, the feasibility and effectiveness of this method was verified by numerical simulations. Numerical simulations show that this method holds the favorable aspects including the advantage of using tiny control gain, the capability of chaotifying across a large range of parametric domain and the high feasibility of the control implement.

Multi-fingered haptic palpation utilizing granular jamming stiffness feedback actuators

International Nuclear Information System (INIS)

Li, Min; Sareh, Sina; Seneviratne, Lakmal D; Wurdemann, Helge A; Althoefer, Kaspar; Ranzani, Tommaso; Dasgupta, Prokar

2014-01-01

This paper describes a multi-fingered haptic palpation method using stiffness feedback actuators for simulating tissue palpation procedures in traditional and in robot-assisted minimally invasive surgery. Soft tissue stiffness is simulated by changing the stiffness property of the actuator during palpation. For the first time, granular jamming and pneumatic air actuation are combined to realize stiffness modulation. The stiffness feedback actuator is validated by stiffness measurements in indentation tests and through stiffness discrimination based on a user study. According to the indentation test results, the introduction of a pneumatic chamber to granular jamming can amplify the stiffness variation range and reduce hysteresis of the actuator. The advantage of multi-fingered palpation using the proposed actuators is proven by the comparison of the results of the stiffness discrimination performance using two-fingered (sensitivity: 82.2%, specificity: 88.9%, positive predicative value: 80.0%, accuracy: 85.4%, time: 4.84 s) and single-fingered (sensitivity: 76.4%, specificity: 85.7%, positive predicative value: 75.3%, accuracy: 81.8%, time: 7.48 s) stiffness feedback. (paper)

Wavelet Methods for Solving Fractional Order Differential Equations

OpenAIRE

A. K. Gupta; S. Saha Ray

2014-01-01

Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linea...

A novel variable stiffness mechanism for dielectric elastomer actuators

Science.gov (United States)

Li, Wen-Bo; Zhang, Wen-Ming; Zou, Hong-Xiang; Peng, Zhi-Ke; Meng, Guang

2017-08-01

In this paper, a novel variable stiffness mechanism is proposed for the design of a variable stiffness dielectric elastomer actuator (VSDEA) which combines a flexible strip with a DEA in a dielectric elastomer minimum energy structure. The DEA induces an analog tuning of the transverse curvature of the strip, thus conveniently providing a voltage-controllable flexural rigidity. The VSDEA tends to be a fully flexible and compact structure with the advantages of simplicity and fast response. Both experimental and theoretical investigations are carried out to reveal the variable stiffness performances of the VSDEA. The effect of the clamped location on the bending stiffness of the VSDEA is analyzed, and then effects of the lengths, the loading points and the applied voltages on the bending stiffness are experimentally investigated. An analytical model is developed to verify the availability of this variable stiffness mechanism, and the theoretical results demonstrate that the bending stiffness of the VSDEA decreases as the applied voltage increases, which agree well with the experimental data. Moreover, the experimental results show that the maximum change of the relative stiffness can reach about 88.80%. It can be useful for the design and optimization of active variable stiffness structures and DEAs for soft robots, vibration control, and morphing applications.

Chemo-mechanical control of neural stem cell differentiation

Science.gov (United States)

Geishecker, Emily R.

Cellular processes such as adhesion, proliferation, and differentiation are controlled in part by cell interactions with the microenvironment. Cells can sense and respond to a variety of stimuli, including soluble and insoluble factors (such as proteins and small molecules) and externally applied mechanical stresses. Mechanical properties of the environment, such as substrate stiffness, have also been suggested to play an important role in cell processes. The roles of both biochemical and mechanical signaling in fate modification of stem cells have been explored independently. However, very few studies have been performed to study well-controlled chemo-mechanotransduction. The objective of this work is to design, synthesize, and characterize a chemo-mechanical substrate to encourage neuronal differentiation of C17.2 neural stem cells. In Chapter 2, Polyacrylamide (PA) gels of varying stiffnesses are functionalized with differing amounts of whole collagen to investigate the role of protein concentration in combination with substrate stiffness. As expected, neurons on the softest substrate were more in number and neuronal morphology than those on stiffer substrates. Neurons appeared locally aligned with an expansive network of neurites. Additional experiments would allow for statistical analysis to determine if and how collagen density impacts C17.2 differentiation in combination with substrate stiffness. Due to difficulties associated with whole protein approaches, a similar platform was developed using mixed adhesive peptides, derived from fibronectin and laminin, and is presented in Chapter 3. The matrix elasticity and peptide concentration can be individually modulated to systematically probe the effects of chemo-mechanical signaling on differentiation of C17.2 cells. Polyacrylamide gel stiffness was confirmed using rheological techniques and found to support values published by Yeung et al. [1]. Cellular growth and differentiation were assessed by cell counts

Lower Body Stiffness Modulation Strategies in Well Trained Female Athletes.

Science.gov (United States)

Millett, Emma L; Moresi, Mark P; Watsford, Mark L; Taylor, Paul G; Greene, David A

2016-10-01

Millett, EL, Moresi, MP, Watsford, ML, Taylor, PG, and Greene, DA. Lower body stiffness modulation strategies in well trained female athletes. J Strength Cond Res 30(10): 2845-2856, 2016-Lower extremity stiffness quantifies the relationship between the amount of leg compression and the external load to which the limb are subjected. This study aimed to assess differences in leg and joint stiffness and the subsequent kinematic and kinetic control mechanisms between athletes from various training backgrounds. Forty-seven female participants (20 nationally identified netballers, 13 high level endurance athletes and 14 age and gender matched controls) completed a maximal unilateral countermovement jump, drop jump and horizontal jump to assess stiffness. Leg stiffness, joint stiffness and associated mechanical parameters were assessed with a 10 camera motion analysis system and force plate. No significant differences were evident for leg stiffness measures between athletic groups for any of the tasks (p = 0.321-0.849). However, differences in joint stiffness and its contribution to leg stiffness, jump performance outcome measures and stiffness control mechanisms were evident between all groups. Practitioners should consider the appropriateness of the task utilised in leg stiffness screening. Inclusion of mechanistic and/or more sports specific tasks may be more appropriate for athletic groups.

Stiffness Evolution in Frozen Sands Subjected to Stress Changes

KAUST Repository

Dai, Sheng; Santamarina, Carlos

2017-01-01

Sampling affects all soils, including frozen soils and hydrate-bearing sediments. The authors monitor the stiffness evolution of frozen sands subjected to various temperature and stress conditions using an oedometer cell instrumented with P-wave transducers. Experimental results show the stress-dependent stiffness of freshly remolded sands, the dominant stiffening effect of ice, creep after unloading, and the associated exponential decrease in stiffness with time. The characteristic time for stiffness loss during creep is of the order of tens of minutes; therefore it is inevitable that frozen soils experience sampling disturbances attributable to unloading. Slow unloading minimizes stiffness loss; conversely, fast unloading causes a pronounced reduction in stiffness probably attributable to the brittle failure of ice or ice-mineral bonding.

Stiffness Evolution in Frozen Sands Subjected to Stress Changes

KAUST Repository

Dai, Sheng

2017-04-21

Sampling affects all soils, including frozen soils and hydrate-bearing sediments. The authors monitor the stiffness evolution of frozen sands subjected to various temperature and stress conditions using an oedometer cell instrumented with P-wave transducers. Experimental results show the stress-dependent stiffness of freshly remolded sands, the dominant stiffening effect of ice, creep after unloading, and the associated exponential decrease in stiffness with time. The characteristic time for stiffness loss during creep is of the order of tens of minutes; therefore it is inevitable that frozen soils experience sampling disturbances attributable to unloading. Slow unloading minimizes stiffness loss; conversely, fast unloading causes a pronounced reduction in stiffness probably attributable to the brittle failure of ice or ice-mineral bonding.

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

Directory of Open Access Journals (Sweden)

Thomas Gomez

2018-04-01

Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

Linear differential equations to solve nonlinear mechanical problems: A novel approach

OpenAIRE

Nair, C. Radhakrishnan

2004-01-01

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

Experimental Challenges to Stiffness as a Transport Paradigm

Science.gov (United States)

Luce, T. C.

2017-10-01

Transport in plasmas is treated experimentally as a relationship between gradients and fluxes in analogy to the random-walk problem. Gyrokinetic models often predict strong increases in local flux for small increases in local gradient when above a threshold, holding all other parameters fixed. This has been named `stiffness'. The radial scalelength is then expected to vary little with source strength as a result of high stiffness. To probe the role of ExB shearing on stiffness in the DIII-D tokamak, two neutral beam injection power scans in H-mode plasmas were specially crafted-one with constant, low torque and one with increasing torque. The ion heat, electron heat, and ion toroidal momentum transport do not show expected signatures of stiffness, while the ion particle transport does. The ion heat transport shows the clearest discrepancy; the normalized heat flux drops with increasing inverse ion temperature scalelength. ExB shearing affects the transport magnitude, but not the scalelength dependence. Linear gyrofluid (TGLF) and nonlinear gyrokinetic (GYRO) predictions show stiff ion heat transport around the experimental profiles. The ion temperature gradient required to match the ion heat flux with increasing auxiliary power is not correctly described by TGLF, even when parameters are varied within the experimental uncertainties. TGLF also underpredicts transport at smaller radii, but overpredicts transport at larger radii. Independent of the theory/experiment comparison, it is not clear that the theoretical definition of stiffness yields any prediction about parameter scans such as the power scans here, because the quantities that must be held fixed to quantify stiffness are varied. A survey of recent literature indicated that profile resilience is routinely attributed to stiffness, but simple model calculations show profile resilience does not imply stiffness. Taken together, these observations challenge the use of local stiffness as a paradigm for explaining

Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations

Science.gov (United States)

Rihan, Fathalla A.; Al-Salti, Nasser S.

2017-09-01

In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.

PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

Korhan KARABULUT

1998-03-01

Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.

Disorder-induced stiffness degradation of highly disordered porous materials

Science.gov (United States)

Laubie, Hadrien; Monfared, Siavash; Radjaï, Farhang; Pellenq, Roland; Ulm, Franz-Josef

2017-09-01

The effective mechanical behavior of multiphase solid materials is generally modeled by means of homogenization techniques that account for phase volume fractions and elastic moduli without considering the spatial distribution of the different phases. By means of extensive numerical simulations of randomly generated porous materials using the lattice element method, the role of local textural properties on the effective elastic properties of disordered porous materials is investigated and compared with different continuum micromechanics-based models. It is found that the pronounced disorder-induced stiffness degradation originates from stress concentrations around pore clusters in highly disordered porous materials. We identify a single disorder parameter, φsa, which combines a measure of the spatial disorder of pores (the clustering index, sa) with the pore volume fraction (the porosity, φ) to scale the disorder-induced stiffness degradation. Thus, we conclude that the classical continuum micromechanics models with one spherical pore phase, due to their underlying homogeneity assumption fall short of addressing the clustering effect, unless additional texture information is introduced, e.g. in form of the shift of the percolation threshold with disorder, or other functional relations between volume fractions and spatial disorder; as illustrated herein for a differential scheme model representative of a two-phase (solid-pore) composite model material.

Mechanical loading regulates human MSC differentiation in a multi-layer hydrogel for osteochondral tissue engineering.

Science.gov (United States)

Steinmetz, Neven J; Aisenbrey, Elizabeth A; Westbrook, Kristofer K; Qi, H Jerry; Bryant, Stephanie J

2015-07-01

A bioinspired multi-layer hydrogel was developed for the encapsulation of human mesenchymal stem cells (hMSCs) as a platform for osteochondral tissue engineering. The spatial presentation of biochemical cues, via incorporation of extracellular matrix analogs, and mechanical cues, via both hydrogel crosslink density and externally applied mechanical loads, were characterized in each layer. A simple sequential photopolymerization method was employed to form stable poly(ethylene glycol)-based hydrogels with a soft cartilage-like layer of chondroitin sulfate and low RGD concentrations, a stiff bone-like layer with high RGD concentrations, and an intermediate interfacial layer. Under a compressive load, the variation in hydrogel stiffness within each layer produced high strains in the soft cartilage-like layer, low strains in the stiff bone-like layer, and moderate strains in the interfacial layer. When hMSC-laden hydrogels were cultured statically in osteochondral differentiation media, the local biochemical and matrix stiffness cues were not sufficient to spatially guide hMSC differentiation after 21 days. However dynamic mechanical stimulation led to differentially high expression of collagens with collagen II in the cartilage-like layer, collagen X in the interfacial layer and collagen I in the bone-like layer and mineral deposits localized to the bone layer. Overall, these findings point to external mechanical stimulation as a potent regulator of hMSC differentiation toward osteochondral cellular phenotypes. Copyright © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Stiffness and damping in mechanical design

National Research Council Canada - National Science Library

Rivin, Eugene I

1999-01-01

... important conceptual issues are stiffness of mechanical structures and their components and damping in mechanical systems sensitive to and/or generating vibrations. Stiffness and strength are the most important criteria for many mechanical designs. However, although there are hundreds of books on various aspects of strength, and strength issues ar...

Direct approach for solving nonlinear evolution and two-point

Indian Academy of Sciences (India)

Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples ...

High-order quantum algorithm for solving linear differential equations

International Nuclear Information System (INIS)

Berry, Dominic W

2014-01-01

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of high-order methods (where the error over a time step is a high power of the size of the time step) to improve the efficiency. These provide scaling close to Δt 2 in the evolution time Δt. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution. (paper)

The Effect of Shoe Insole Stiffness on Leg Stiffness during Stance Phase of Running in Two Different Speeds ‎among Active Men

Directory of Open Access Journals (Sweden)

Zeinab Tazike-Lemeski

2016-08-01

Full Text Available Introduction: The effect of shoe insoles with different characteristics and in different running speeds on lower-limb stiffness is still ‎controversial. The aim of this study was to investigate the effect of two types of insoles (soft and semi-rigid in two ‎different running speeds on leg stiffness during stance phase of running among active men.‎ Materials and Methods: ‎15 male students without any background of lower extremity injury were selected. Subjects were asked to run with ‎two controlled velocities of 3.0 ± 0.2 and 5.0 ± 0.1 m/s in control and insole conditions (soft and semi-rigid on a ‎force plate, placed on the middle of 15-meter runway. The cinematics and cinetics of motion were measured and ‎calculated using 5 video cameras and one force plate. The leg stiffness was achieved via dividing the vertical ‎ground reaction force by leg compression. Two-factor repeated measures ANOVA was used to test the hypothesis at ‎the significance level of P £ 0.050.‎ Results: There was a significant difference between the two types of insoles on leg stiffness. In fact, semi-rigid insole significantly increased leg stiffness (P < 0.001. However, this discrepancy was not related to the running speed (P = 0.999. In addition, there was no significant difference between the two different speeds on leg stiffness (P = 0.632. Conclusion: It seems that the increase in shoe insole stiffness may increase the leg stiffness. Furthermore, the effect of insole ‎stiffness is not related to the running speed, and leg stiffness will remains constant in low to medium running speeds.‎

Solving of L0 norm constrained EEG inverse problem.

Science.gov (United States)

Xu, Peng; Lei, Xu; Hu, Xiao; Yao, Dezhong

2009-01-01

l(0) norm is an effective constraint used to solve EEG inverse problem for a sparse solution. However, due to the discontinuous and un-differentiable properties, it is an open issue to solve the l(0) norm constrained problem, which is usually instead solved by using some alternative functions like l(1) norm to approximate l(0) norm. In this paper, a continuous and differentiable function having the same form as the transfer function of Butterworth low-pass filter is introduced to approximate l(0) norm constraint involved in EEG inverse problem. The new approximation based approach was compared with l(1) norm and LORETA solutions on a realistic head model using simulated sources. The preliminary results show that this alternative approximation to l(0) norm is promising for the estimation of EEG sources with sparse distribution.

Auxiliary equation method for solving nonlinear partial differential equations

International Nuclear Information System (INIS)

Sirendaoreji,; Jiong, Sun

2003-01-01

By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

Thyrotropin serum levels are differentially associated with biochemical markers of bone turnover and stiffness in women and men: results from the SHIP cohorts.

Science.gov (United States)

Tsourdi, E; Wallaschofski, H; Rauner, M; Nauck, M; Pietzner, M; Rettig, R; Ittermann, T; Völzke, H; Völker, U; Hofbauer, L C; Hannemann, A

2016-02-01

In two large German population-based cohorts, we showed positive associations between serum thyrotropin (TSH) concentrations and the Fracture Risk Assessment score (FRAX) in men and positive associations between TSH concentrations and bone turnover markers in women. The role of thyroid hormones on bone stiffness and turnover is poorly defined. Existing studies are confounded by differences in design and small sample size. We assessed the association between TSH serum concentrations and bone stiffness and turnover in the SHIP cohorts, which are two population-based cohorts from a region in Northern Germany comprising 2654 men and women and 3261 men and women, respectively. We calculated the bone stiffness index using quantitative ultrasound (QUS) at the calcaneus, employed FRAX score for assessment of major osteoporotic fractures, and measured bone turnover markers, N-terminal propeptide of type I procollagen (P1NP), bone-specific alkaline phosphatase (BAP), osteocalcin, and type I collagen cross-linked C-telopeptide (CTX) in all subjects and sclerostin in a representative subgroup. There was no association between TSH concentrations and the stiffness index in both genders. In men, TSH correlated positively with the FRAX score both over the whole TSH range (p < 0.01) and within the reference TSH range (p < 0.01). There were positive associations between TSH concentrations and P1NP, BAP, osteocalcin, and CTX (p < 0.01) in women but not in men. There was no significant association between TSH and sclerostin levels. TSH serum concentrations are associated with gender-specific changes in bone turnover and stiffness.

A uniform quantitative stiff stability estimate for BDF schemes

Directory of Open Access Journals (Sweden)

Winfried Auzinger

2006-01-01

Full Text Available The concepts of stability regions, \\(A\\- and \\(A(\\alpha\\-stability - albeit based on scalar models - turned out to be essential for the identification of implicit methods suitable for the integration of stiff ODEs. However, for multistep methods, knowledge of the stability region provides no information on the quantitative stability behavior of the scheme. In this paper we fill this gap for the important class of Backward Differentiation Formulas (BDF. Quantitative stability bounds are derived which are uniformly valid in the stability region of the method. Our analysis is based on a study of the separation of the characteristic roots and a special similarity decomposition of the associated companion matrix.

How to make university students solve physics problems requiring mathematical skills: The "Adventurous Problem Solving" approach

NARCIS (Netherlands)

de Mul, F.F.M.; Martin Batlle, C.; Martin i Batlle, Cristina; de Bruijn, Imme; Rinzema, K.; Rinzema, Kees

2003-01-01

Teaching physics to first-year university students (in the USA: junior/senior level) is often hampered by their lack of skills in the underlying mathematics, and that in turn may block their understanding of the physics and their ability to solve problems. Examples are vector algebra, differential

The stable stiffness triangle - drained sand during deformation cycles

DEFF Research Database (Denmark)

Sabaliauskas, Tomas; Ibsen, Lars Bo

2017-01-01

Cyclic, drained sand stiffness was observed using the Danish triaxial appa- ratus. New, deformation dependant soil property (the stable stiffness triangle) was detected. Using the the stable stiffness triangle, secant stiffness of drained sand was plausible to predict (and control) even during ir...... findings can find application in off-shore, seismic and other engi- neering practice, or inspire new branches of research and modelling wherever dynamic, cyclic or transient loaded sand is encountered....

Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

Energy Technology Data Exchange (ETDEWEB)

Jin Chen

2009-12-07

Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

Pipe elbow stiffness coefficients including shear and bend flexibility factors for use in direct stiffness codes

International Nuclear Information System (INIS)

Perry, R.F.

1977-01-01

Historically, developments of computer codes used for piping analysis were based upon the flexibility method of structural analysis. Because of the specialized techniques employed in this method, the codes handled systems composed of only piping elements. Over the past ten years, the direct stiffness method has gained great popularity because of its systematic solution procedure regardless of the type of structural elements composing the system. A great advantage is realized with a direct stiffness code that combines piping elements along with other structural elements such as beams, plates, and shells, in a single model. One common problem, however, has been the lack of an accurate pipe elbow element that would adequately represent the effects of transverse shear and bend flexibility factors. The purpose of the present paper is to present a systematic derivation of the required 12x12 stiffness matrix and load vectors for a three dimensional pipe elbow element which includes the effects of transverse shear and pipe bend flexibility according to the ASME Boiler and Pressure Vessel Code, Section III. The results are presented analytically and as FORTRAN subroutines to be directly incorporated into existing direct stiffness codes. (Auth.)

Direct measurement of the intrinsic ankle stiffness during standing

NARCIS (Netherlands)

Vlutters, Mark; Vlutters, M.; Boonstra, Tjitske; Schouten, Alfred Christiaan; van der Kooij, Herman

2015-01-01

Ankle stiffness contributes to standing balance, counteracting the destabilizing effect of gravity. The ankle stiffness together with the compliance between the foot and the support surface make up the ankle-foot stiffness, which is relevant to quiet standing. The contribution of the intrinsic

Integration of differential equations by the pseudo-linear (PL) approximation

International Nuclear Information System (INIS)

Bonalumi, Riccardo A.

1998-01-01

A new method of integrating differential equations was originated with the technique of approximately calculating the integrals called the pseudo-linear (PL) procedure: this method is A-stable. This article contains the following examples: 1st order ordinary differential equations (ODEs), 2nd order linear ODEs, stiff system of ODEs (neutron kinetics), one-dimensional parabolic (diffusion) partial differential equations. In this latter case, this PL method coincides with the Crank-Nicholson method

Biomechanical constraints on the feedforward regulation of endpoint stiffness.

Science.gov (United States)

Hu, Xiao; Murray, Wendy M; Perreault, Eric J

2012-10-01

Although many daily tasks tend to destabilize arm posture, it is still possible to have stable interactions with the environment by regulating the multijoint mechanics of the arm in a task-appropriate manner. For postural tasks, this regulation involves the appropriate control of endpoint stiffness, which represents the stiffness of the arm at the hand. Although experimental studies have been used to evaluate endpoint stiffness control, including the orientation of maximal stiffness, the underlying neural strategies remain unknown. Specifically, the relative importance of feedforward and feedback mechanisms has yet to be determined due to the difficulty separately identifying the contributions of these mechanisms in human experiments. This study used a previously validated three-dimensional musculoskeletal model of the arm to quantify the degree to which the orientation of maximal endpoint stiffness could be changed using only steady-state muscle activations, used to represent feedforward motor commands. Our hypothesis was that the feedforward control of endpoint stiffness orientation would be significantly constrained by the biomechanical properties of the musculoskeletal system. Our results supported this hypothesis, demonstrating substantial biomechanical constraints on the ability to regulate endpoint stiffness throughout the workspace. The ability to regulate stiffness orientation was further constrained by additional task requirements, such as the need to support the arm against gravity or exert forces on the environment. Together, these results bound the degree to which slowly varying feedforward motor commands can be used to regulate the orientation of maximum arm stiffness and provide a context for better understanding conditions in which feedback control may be needed.

Fast RBF OGr for solving PDEs on arbitrary surfaces

Science.gov (United States)

Piret, Cécile; Dunn, Jarrett

2016-10-01

The Radial Basis Functions Orthogonal Gradients method (RBF-OGr) was introduced in [1] to discretize differential operators defined on arbitrary manifolds defined only by a point cloud. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent complex geometries in any spatial dimension. A large limitation of the RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this paper, we apply the RBF-Finite Difference (RBF-FD) technique to the RBF-OGr method for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami operator. This method can be applied to solving PDEs on arbitrary surfaces embedded in ℛ3. We illustrate the accuracy of our new method by solving the heat equation on the unit sphere.

The study of stiffness modulus values for AC-WC pavement

Science.gov (United States)

Lubis, AS; Muis, Z. A.; Iskandar, T. D.

2018-02-01

One of the parameters of the asphalt mixture in order for the strength and durability to be achieved as required is the stress-and-strain showing the stiffness of a material. Stiffness modulus is a very necessary factor that will affect the performance of asphalt pavements. If the stiffness modulus value decreases there will be a cause of aging asphalt pavement crack easily when receiving a heavy load. The high stiffness modulus asphalt concrete causes more stiff and resistant to bending. The stiffness modulus value of an asphalt mixture material can be obtained from the theoretical (indirect methods) and laboratory test results (direct methods). For the indirect methods used Brown & Brunton method, and Shell Bitumen method; while for the direct methods used the UMATTA tool. This study aims to determine stiffness modulus values for AC-WC pavement. The tests were conducted in laboratory that used 3 methods, i.e. Brown & Brunton Method, Shell Bitumen Method and Marshall Test as a substitute tool for the UMATTA tool. Hotmix asphalt made from type AC-WC with pen 60/70 using a mixture of optimum bitumen content was 5.84% with a standard temperature variation was 60°C and several variations of temperature that were 30, 40, 50, 70 and 80°C. The stiffness modulus value results obtained from Brown & Brunton Method, Shell Bitumen Method and Marshall Test which were 1374,93 Mpa, 235,45 Mpa dan 254,96 Mpa. The stiffness modulus value decreases with increasing temperature of the concrete asphalt. The stiffness modulus value from the Bitumen Shell method and the Marshall Test has a relatively similar value.The stiffness modulus value from the Brown & Brunton method is greater than the Bitumen Shell method and the Marshall Test, but can not measure the stiffness modulus value at temperature above 80°C.

STRAP-2, Stress Analysis of Structure with Static Loading by Finite Elements Method. STRAP-D, Stress Analysis of Structure with Time-Dependent Loading by Finite Elements Method

International Nuclear Information System (INIS)

Dearien, J.A.; Uldrich, E.D.

1975-01-01

1 - Description of problem or function: The code STRAP (Structural Analysis Package) was developed to analyze the response of structural systems to static and dynamic loading conditions. STRAP-S solves for the displacements and member forces of structural systems under static loads and temperature gradients. STRAP-D will solve numerically a given structural dynamics problem. 2 - Method of solution: STRAP-S generates the stiffness matrix of a structure by the finite element method and solves the resulting equations for structural displacements and member forces. STRAP-D generates the stiffness matrix, solves for eigenvalues and eigenvectors, uncouples and solves the series of second-order ordinary differential equations, and then calculates and plots the requested member forces. 3 - Restrictions on the complexity of the problem: STRAP-S maxima: 250 degrees of freedom, 100 members; STRAP-D maxima: 100 degrees of freedom, 80 time-steps in the forcing function input

Mesenchymal stem cell adhesion but not plasticity is affected by high substrate stiffness

Directory of Open Access Journals (Sweden)

Janice Kal Van Tam, Koichiro Uto, Mitsuhiro Ebara, Stefania Pagliari, Giancarlo Forte and Takao Aoyagi

2012-01-01

Full Text Available The acknowledged ability of synthetic materials to induce cell-specific responses regardless of biological supplies provides tissue engineers with the opportunity to find the appropriate materials and conditions to prepare tissue-targeted scaffolds. Stem and mature cells have been shown to acquire distinct morphologies in vitro and to modify their phenotype when grown on synthetic materials with tunable mechanical properties. The stiffness of the substrate used for cell culture is likely to provide cells with mechanical cues mimicking given physiological or pathological conditions, thus affecting the biological properties of cells. The sensitivity of cells to substrate composition and mechanical properties resides in multiprotein complexes called focal adhesions, whose dynamic modification leads to cytoskeleton remodeling and changes in gene expression. In this study, the remodeling of focal adhesions in human mesenchymal stem cells in response to substrate stiffness was followed in the first phases of cell–matrix interaction, using poly-ε-caprolactone planar films with similar chemical composition and different elasticity. As compared to mature dermal fibroblasts, mesenchymal stem cells showed a specific response to substrate stiffness, in terms of adhesion, as a result of differential focal adhesion assembly, while their multipotency as a bulk was not significantly affected by matrix compliance. Given the sensitivity of stem cells to matrix mechanics, the mechanobiology of such cells requires further investigations before preparing tissue-specific scaffolds.

Solving Bi-Objective Optimal Power Flow using Hybrid method of Biogeography-Based Optimization and Differential Evolution Algorithm: A case study of the Algerian Electrical Network

Directory of Open Access Journals (Sweden)

Ouafa Herbadji

2016-03-01

Full Text Available This paper proposes a new hybrid metaheuristique algorithm based on the hybridization of Biogeography-based optimization with the Differential Evolution for solving the optimal power flow problem with emission control. The biogeography-based optimization (BBO algorithm is strongly influenced by equilibrium theory of island biogeography, mainly through two steps: Migration and Mutation. Differential Evolution (DE is one of the best Evolutionary Algorithms for global optimization. The hybridization of these two methods is used to overcome traps of local optimal solutions and problems of time consumption. The objective of this paper is to minimize the total fuel cost of generation, total emission, total real power loss and also maintain an acceptable system performance in terms of limits on generator real power, bus voltages and power flow of transmission lines. In the present work, BBO/DE has been applied to solve the optimal power flow problems on IEEE 30-bus test system and the Algerian electrical network 114 bus. The results obtained from this method show better performances compared with DE, BBO and other well known metaheuristique and evolutionary optimization methods.

Simvastatin Ameliorates Matrix Stiffness-Mediated Endothelial Monolayer Disruption.

Directory of Open Access Journals (Sweden)

Marsha C Lampi

Full Text Available Arterial stiffening accompanies both aging and atherosclerosis, and age-related stiffening of the arterial intima increases RhoA activity and cell contractility contributing to increased endothelium permeability. Notably, statins are 3-hydroxy-3-methylglutaryl coenzyme A (HMG-CoA reductase inhibitors whose pleiotropic effects include disrupting small GTPase activity; therefore, we hypothesized the statin simvastatin could be used to attenuate RhoA activity and inhibit the deleterious effects of increased age-related matrix stiffness on endothelial barrier function. Using polyacrylamide gels with stiffnesses of 2.5, 5, and 10 kPa to mimic the physiological stiffness of young and aged arteries, endothelial cells were grown to confluence and treated with simvastatin. Our data indicate that RhoA and phosphorylated myosin light chain activity increase with matrix stiffness but are attenuated when treated with the statin. Increases in cell contractility, cell-cell junction size, and indirect measurements of intercellular tension that increase with matrix stiffness, and are correlated with matrix stiffness-dependent increases in monolayer permeability, also decrease with statin treatment. Furthermore, we report that simvastatin increases activated Rac1 levels that contribute to endothelial barrier enhancing cytoskeletal reorganization. Simvastatin, which is prescribed clinically due to its ability to lower cholesterol, alters the endothelial cell response to increased matrix stiffness to restore endothelial monolayer barrier function, and therefore, presents a possible therapeutic intervention to prevent atherogenesis initiated by age-related arterial stiffening.

Solving Variable Coefficient Fourth-Order Parabolic Equation by ...

African Journals Online (AJOL)

Solving Variable Coefficient Fourth-Order Parabolic Equation by Modified initial guess Variational ... variable coefficient fourth order parabolic partial differential equations. The new method shows rapid convergence to the exact solution.

Analysis of Dynamic Stiffness of Bridge Cap-Pile System

Directory of Open Access Journals (Sweden)

Jinhui Chu

2018-01-01

Full Text Available In order to investigate the applicability of dynamic stiffness for bridge cap-pile system, a laboratory test was performed. A numerical model was also built for this type of system. The impact load was applied on the cap top and the dynamic stiffness was analysed. Then, the effect of the effective friction area between pile and soil was also considered. Finally, the dynamic stiffness relationship between the single pile and the cap-pile system was also compared. The results show that the dynamic stiffness is a sensitive index and can well reflect the static characteristics of the pile at the elastic stage. There is a significant positive correlation between the vertical dynamic stiffness index and bearing capacity of the cap-pile system in the similar formation environment. For the cap-pile system with four piles, the dynamic stiffness is about four times as large as the single pile between 10 and 20 Hz.

Stiff quantum polymers

OpenAIRE

Kleinert, H.

2009-01-01

At ultralow temperatures, polymers exhibit quantum behavior, which is calculated here for the second and fourth moments of the end-to-end distribution in the large-stiffness regime. The result should be measurable for polymers in wide optical traps.

Arterial Stiffness in Children: Pediatric Measurement and Considerations

Science.gov (United States)

Savant, Jonathan D.; Furth, Susan L.; Meyers, Kevin E.C.

2014-01-01

Background Arterial stiffness is a natural consequence of aging, accelerated in certain chronic conditions, and predictive of cardiovascular events in adults. Emerging research suggests the importance of arterial stiffness in pediatric populations. Methods There are different indices of arterial stiffness. The present manuscript focuses on carotid-femoral pulse wave velocity and pulse wave analysis, although other methodologies are discussed. Also reviewed are specific measurement considerations for pediatric populations and the literature describing arterial stiffness in children with certain chronic conditions (primary hypertension, obesity, diabetes, chronic kidney disease, hypercholesterolemia, genetic syndromes involving vasculopathy, and solid organ transplant recipients). Conclusions The measurement of arterial stiffness in children is feasible and, under controlled conditions, can give accurate information about the underlying state of the arteries. This potentially adds valuable information about the functionality of the cardiovascular system in children with a variety of chronic diseases well beyond that of the brachial artery blood pressure. PMID:26587447

Numerical Analysis of Partial Differential Equations

CERN Document Server

Lui, S H

2011-01-01

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis

Reduced differential transform method for partial differential equations within local fractional derivative operators

Directory of Open Access Journals (Sweden)

Hossein Jafari

2016-04-01

Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

Integral transform method for solving time fractional systems and fractional heat equation

Directory of Open Access Journals (Sweden)

Arman Aghili

2014-01-01

Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

Differential Equation over Banach Algebra

OpenAIRE

Kleyn, Aleks

2018-01-01

In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

A gradient based algorithm to solve inverse plane bimodular problems of identification

Science.gov (United States)

Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

2018-02-01

This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

Stopping test of iterative methods for solving PDE

International Nuclear Information System (INIS)

Wang Bangrong

1991-01-01

In order to assure the accuracy of the numerical solution of the iterative method for solving PDE (partial differential equation), the stopping test is very important. If the coefficient matrix of the system of linear algebraic equations is strictly diagonal dominant or irreducible weakly diagonal dominant, the stopping test formulas of the iterative method for solving PDE is proposed. Several numerical examples are given to illustrate the applications of the stopping test formulas

Plant fibre composites - porosity and stiffness

DEFF Research Database (Denmark)

Madsen, Bo; Thygesen, Anders; Lilholt, Hans

2009-01-01

Plant fibre composites contain typically a relatively large amount of porosity which influences their performance. A model, based on a modified rule of mixtures, is presented to include the influence of porosity on the composite stiffness. The model integrates the volumetric composition...... of the composites with their mechanical properties. The fibre weight fraction is used as an independent parameter to calculate the complete volumetric composition. A maximum obtainable stiffness of the composites is calculated at a certain transition fibre weight fraction, which is characterised by a best possible...... combination of high fibre volume fraction and low porosity. The model is validated with experimental data from the literature on several types of composites. A stiffness diagram is presented to demonstrate that the calculations can be used for tailoring and design of composites with a given profile...

Is chronic obstructive pulmonary disease associated with increased arterial stiffness?

DEFF Research Database (Denmark)

Janner, Julie H; McAllister, David A; Godtfredsen, Nina S

2012-01-01

We hypothesize that airflow limitation is associated with increasing arterial stiffness and that having COPD increases a non-invasive measure of arterial stiffness - the aortic augmentation index (AIx) - independently of other CVD risk factors.......We hypothesize that airflow limitation is associated with increasing arterial stiffness and that having COPD increases a non-invasive measure of arterial stiffness - the aortic augmentation index (AIx) - independently of other CVD risk factors....

Formal Solutions for Polarized Radiative Transfer. III. Stiffness and Instability

Science.gov (United States)

Janett, Gioele; Paganini, Alberto

2018-04-01

Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which potentially results in numerical instability. This negatively impacts the accuracy of formal solvers, and small step-sizes are often necessary to retrieve physical solutions. This work presents stability analyses of formal solvers for the radiative transfer equation of polarized light, identifies instability issues, and suggests practical remedies. In particular, the assumptions and the limitations of the stability analysis of Runge–Kutta methods play a crucial role. On this basis, a suitable and pragmatic formal solver is outlined and tested. An insightful comparison to the scalar radiative transfer equation is also presented.

Damper modules with adapted stiffness ratio

Energy Technology Data Exchange (ETDEWEB)

Sonnenburg, R.; Stretz, A. [ZF Sachs AG, Entwicklungszentrum, Schweinfurt (Germany)

2011-07-15

A mechanism for the excitation of piston rod vibrations in automotive damper modules is discussed by a simple model. An improved nonlinear model based on elasticity effects leads to good simulation results. It is shown theoretically and experimentally that the adaptation of the stiffness of the piston rod bushing to the ''stiffness'' of the damper force characteristic can eliminate the piston rod oscillations completely. (orig.)

Rotational and peak torque stiffness of rugby shoes.

Science.gov (United States)

Ballal, Moez S; Usuelli, Federico Giuseppe; Montrasio, Umberto Alfieri; Molloy, Andy; La Barbera, Luigi; Villa, Tomaso; Banfi, Giuseppe

2014-09-01

Sports people always strive to avoid injury. Sports shoe designs in many sports have been shown to affect traction and injury rates. The aim of this study is to demonstrate the differing stiffness and torque in rugby boots that are designed for the same effect. Five different types of rugby shoes commonly worn by scrum forwards were laboratory tested for rotational stiffness and peak torque on a natural playing surface generating force patterns that would be consistent with a rugby scrum. The overall internal rotation peak torque was 57.75±6.26 Nm while that of external rotation was 56.55±4.36 Nm. The Peak internal and external rotational stiffness were 0.696±0.1 and 0.708±0.06 Nm/deg respectively. Our results, when compared to rotational stiffness and peak torques of football shoes published in the literature, show that shoes worn by rugby players exert higher rotational and peak torque stiffness compared to football shoes when tested on the same natural surfaces. There was significant difference between the tested rugby shoes brands. In our opinion, to maximize potential performance and lower the potential of non-contact injury, care should be taken in choosing boots with stiffness appropriate to the players main playing role. Copyright © 2014 Elsevier Ltd. All rights reserved.

Static stiffness modeling of a novel hybrid redundant robot machine

International Nuclear Information System (INIS)

Li Ming; Wu Huapeng; Handroos, Heikki

2011-01-01

This paper presents a modeling method to study the stiffness of a hybrid serial-parallel robot IWR (Intersector Welding Robot) for the assembly of ITER vacuum vessel. The stiffness matrix of the basic element in the robot is evaluated using matrix structural analysis (MSA); the stiffness of the parallel mechanism is investigated by taking account of the deformations of both hydraulic limbs and joints; the stiffness of the whole integrated robot is evaluated by employing the virtual joint method and the principle of virtual work. The obtained stiffness model of the hybrid robot is analytical and the deformation results of the robot workspace under certain external load are presented.

Stiffness requirement of flexible skin for variable trailing-edge camber wing

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

The method for analyzing the deformation of flexible skin under the air loads was developed based on the panel method and finite element method.The deformation of flexible skin under air pressures and effects of the local deformation on the aerodynamic characteristics were discussed.Numerical results show that the flexible skin on the upper surface of trailing-edge will bubble under the air loads and the bubble has a powerful effect on the aerodynamic pressure near the surface of local deforma-tion.Then the stiffness requirements for flexible skin of variable trailing-edge were given by using the Jacobs rule,i.e.,the maximum displacement of skin is not greater than 0.1% of wing chord.Results show that the in-plane stiffness can be reduced by increasing the ratio of bending stiffness to in-plane stiffness.Although the deformation of flexible skin increases with the in-plane stiffness decreasing,it depends on the bending stiffness.When the bending stiffness exceeds critical value,the deformation of flexible skin only depends on the bending stiffness and has nothing to do with the in-plane stiffness.The conclusions can be used for the structural design of flexible skin.

Subspace methods for identification of human ankle joint stiffness.

Science.gov (United States)

Zhao, Y; Westwick, D T; Kearney, R E

2011-11-01

Joint stiffness, the dynamic relationship between the angular position of a joint and the torque acting about it, describes the dynamic, mechanical behavior of a joint during posture and movement. Joint stiffness arises from both intrinsic and reflex mechanisms, but the torques due to these mechanisms cannot be measured separately experimentally, since they appear and change together. Therefore, the direct estimation of the intrinsic and reflex stiffnesses is difficult. In this paper, we present a new, two-step procedure to estimate the intrinsic and reflex components of ankle stiffness. In the first step, a discrete-time, subspace-based method is used to estimate a state-space model for overall stiffness from the measured overall torque and then predict the intrinsic and reflex torques. In the second step, continuous-time models for the intrinsic and reflex stiffnesses are estimated from the predicted intrinsic and reflex torques. Simulations and experimental results demonstrate that the algorithm estimates the intrinsic and reflex stiffnesses accurately. The new subspace-based algorithm has three advantages over previous algorithms: 1) It does not require iteration, and therefore, will always converge to an optimal solution; 2) it provides better estimates for data with high noise or short sample lengths; and 3) it provides much more accurate results for data acquired under the closed-loop conditions, that prevail when subjects interact with compliant loads.

Influence of stiffness on CHF for horizontal tubes under LPLF conditions

Energy Technology Data Exchange (ETDEWEB)

Baburajan, P.K. [Nuclear Safety Analysis Division, AERB, Niyamak Bhavan, 400094 (India); Bisht, Govind Singh [Department of Mechanical Engineering, IIT Bombay, 400076 (India); Gaikwad, Avinash J. [Nuclear Safety Analysis Division, AERB, Niyamak Bhavan, 400094 (India); Prabhu, S.V., E-mail: svprabhu@iitb.ac.in [Department of Mechanical Engineering, IIT Bombay, 400076 (India)

2014-10-01

Highlights: • Effect of stiffness on the CHF in horizontal tube under LPLF conditions is studied. • CHF increases with the increase in stiffness. • Correlation for the prediction of CHF as a function of stiffness is developed. • Correlation for mass flux at CHF in terms of stiffness and initial mass flux is given. • RELAP5 is capable of predicting the effect of stiffness on CHF. - Abstract: Studies reported in the past on critical heat flux (CHF) are mostly limited to vertical flow, large channel diameter, high pressure and high mass flux. Since horizontal flow is commonly encountered in boiler tubes, refrigerating equipments and nuclear reactor fuel channels (PHWR), there is a need to understand horizontal flow CHF, generate sufficient experimental database and to develop reliable predictive method. Few studies are reported on the effect of upstream flow restrictions on flow instabilities and CHF. The present work investigates the effect of upstream flow restriction on CHF in horizontal flow at near atmospheric pressure conditions. In the present study, stiffness is defined as the ratio of upstream flow restriction pressure drop to the test section pressure drop. The classification of a flow boiling system as soft or stiff on the basis of quantification of the stiffness is attempted. Experimental data shows an increase in the CHF with the increase in the stiffness for a given initial mass flux. A correlation for the prediction of CHF under various stiffness conditions is developed. A correlation is suggested to predict the mass flux at CHF as a function of stiffness and initial mass flux. Modeling and transient analysis of the stiffness effect on CHF is carried out using the thermal hydraulic system code RELAP5. The predicted phenomena are in agreement with the experimental observations.

Fatigue crack paths under the influence of changes in stiffness

Directory of Open Access Journals (Sweden)

G. Kullmer

2016-02-01

Full Text Available An important topic of the Collaborative Research Centre TRR 30 of the Deutsche Forschungsgemeinschaft (DFG is the crack growth behaviour in graded materials. In addition, the growth of cracks in the neighbourhood of regions and through regions with different material properties belongs under this topic. Due to the different material properties, regions with differing stiffness compared to the base material may arise. Regions with differing stiffness also arise from ribs, grooves or boreholes. Since secure findings on the propagation behaviour of fatigue cracks are essential for the evaluation of the safety of components and structures, the growth of cracks near changes in stiffness has to be considered, too. Depending on the way a crack penetrates the zone of influence of such a change in stiffness and depending on whether this region is more compliant or stiffer than the surrounding area the crack may grow towards or away from this region. Both cases result in curved crack paths that cannot be explained only by the global loading situation. To evaluate the influence of regions with differing stiffness on the path of fatigue cracks the paths and the stress intensity factors of cracks growing near and through regions with differing stiffness are numerically determined with the program system ADAPCRACK3D. Therefore, arrangements of changes in stiffness modelled as material inclusions with stiffness properties different from the base material or modelled as ribs and grooves are systematically varied to develop basic conclusions about the crack growth behaviour near and through changes in stiffness.

On prestress stiffness analysis of bolt-plate contact assemblies

DEFF Research Database (Denmark)

Pedersen, Niels Leergaard; Pedersen, Pauli

2008-01-01

, but with finite element (FE) and contact analysis, it is possible to find the stiffness of the member. In the case of many connections and for practical applications, it is not suitable to make a full FE analysis. The purpose of the present paper is to find simplified expressions for the stiffness of the member......, including the case when the width of the member is limited. The calculation of the stiffness is based on the FE, including the solution to the contact problem, and we express the stiffness as a function of the elastic energy in the structure, whereby the definition of the displacements related...

Low frequency noise reduction using stiff light composite panels

Institute of Scientific and Technical Information of China (English)

DENG Yongchang; LIN Weizheng

2003-01-01

The experiment presented in this paper is to investigate and analyze the noise reduction at low frequency using stiff light composite panels. Since these composite panels are made of lightweight and stiff materials, this actuation strategy will enable the creation of composite panels for duct noise control without using traditional heavy structural mass. The results suggest that the mass-spring resonance absorption in the case of a comparatively stiff thick panel with a thin flexible plate is more efficient with minimum weight, when subjected to low-frequency (<500 Hz). The efficiency of the panel absorber depends on the mass of the thin flexible plate and the stiffness of the panel.

Elastin in large artery stiffness and hypertension

Science.gov (United States)

Wagenseil, Jessica E.; Mecham, Robert P.

2012-01-01

Large artery stiffness, as measured by pulse wave velocity (PWV), is correlated with high blood pressure and may be a causative factor in essential hypertension. The extracellular matrix components, specifically the mix of elastin and collagen in the vessel wall, determine the passive mechanical properties of the large arteries. Elastin is organized into elastic fibers in the wall during arterial development in a complex process that requires spatial and temporal coordination of numerous proteins. The elastic fibers last the lifetime of the organism, but are subject to proteolytic degradation and chemical alterations that change their mechanical properties. This review discusses how alterations in the amount, assembly, organization or chemical properties of the elastic fibers affect arterial stiffness and blood pressure. Strategies for encouraging or reversing alterations to the elastic fibers are addressed. Methods for determining the efficacy of these strategies, by measuring elastin amounts and arterial stiffness, are summarized. Therapies that have a direct effect on arterial stiffness through alterations to the elastic fibers in the wall may be an effective treatment for essential hypertension. PMID:22290157

Advanced damper with negative structural stiffness elements

International Nuclear Information System (INIS)

Dong, Liang; Lakes, Roderic S

2012-01-01

Negative stiffness is understood as the occurrence of a force in the same direction as the imposed deformation. Structures and composites with negative stiffness elements enable a large amplification in damping. It is shown in this work, using an experimental approach, that when a flexible flat-ends column is aligned in a post-buckled condition, a negative structural stiffness and large hysteresis (i.e., high damping) can be achieved provided the ends of the column undergo tilting from flat to edge contact. Stable axial dampers with initial modulus equivalent to that of the parent material and with enhanced damping were designed and built using constrained negative stiffness effects entailed by post-buckled press-fit flat-ends columns. Effective damping of approximately 1 and an effective stiffness–damping product of approximately 1.3 GPa were achieved in such stable axial dampers consisting of PMMA columns. This is a considerable improvement for this figure of merit (i.e., the stiffness–damping product), which generally cannot exceed 0.6 GPa for currently used damping layers. (paper)

Evaluating pulp stiffness from fibre bundles by ultrasound

Science.gov (United States)

Karppinen, Timo; Montonen, Risto; Määttänen, Marjo; Ekman, Axel; Myllys, Markko; Timonen, Jussi; Hæggström, Edward

2012-06-01

A non-destructive ultrasonic tester was developed to measure the stiffness of pulp bundles. The mechanical properties of pulp are important when estimating the behaviour of paper under stress. Currently available pulp tests are tedious and alter the fibres structurally and mechanically. The developed tester employs (933 ± 15) kHz tweezer-like ultrasonic transducers and time-of-flight measurement through (9.0 ± 2.5) mm long and (0.8 ± 0.1) mm thick fibre bundles kept at (19.1 ± 0.4) °C and (62 ± 1)% RH. We determined the stiffness of soft wood pulps produced by three kraft pulping modifications: standard kraft pulp, (5.2 ± 0.4) GPa, prehydrolysis kraft pulp, (4.3 ± 0.4) GPa, and alkali extracted prehydrolysis kraft pulp, (3.3 ± 0.4) GPa. Prehydrolysis and alkali extraction processes mainly lowered the hemicellulose content of the pulps, which essentially decreased the fibre-wall stiffness hence impairing the stiffness of the fibre networks. Our results indicate that the method allows ranking of pulps according to their stiffness determined from bundle-like samples taken at an early phase of the papermaking process.

A new variable stiffness suspension system: passive case

Directory of Open Access Journals (Sweden)

O. M. Anubi

2013-02-01

Full Text Available This paper presents the design, analysis, and experimental validation of the passive case of a variable stiffness suspension system. The central concept is based on a recently designed variable stiffness mechanism. It consists of a horizontal control strut and a vertical strut. The main idea is to vary the load transfer ratio by moving the location of the point of attachment of the vertical strut to the car body. This movement is controlled passively using the horizontal strut. The system is analyzed using an L2-gain analysis based on the concept of energy dissipation. The analyses, simulation, and experimental results show that the variable stiffness suspension achieves better performance than the constant stiffness counterpart. The performance criteria used are; ride comfort, characterized by the car body acceleration, suspension deflection, and road holding, characterized by tire deflection.

Association of Parental Hypertension With Arterial Stiffness in Nonhypertensive Offspring

DEFF Research Database (Denmark)

Andersson, Charlotte; Quiroz, Rene; Enserro, Danielle

2016-01-01

High arterial stiffness seems to be causally involved in the pathogenesis of hypertension. We tested the hypothesis that offspring of parents with hypertension may display higher arterial stiffness before clinically manifest hypertension, given that hypertension is a heritable condition. We compa......, in this community-based sample of young, nonhypertensive adults, we observed greater arterial stiffness in offspring of parents with hypertension. These observations are consistent with higher vascular stiffness at an early stage in the pathogenesis of hypertension.......High arterial stiffness seems to be causally involved in the pathogenesis of hypertension. We tested the hypothesis that offspring of parents with hypertension may display higher arterial stiffness before clinically manifest hypertension, given that hypertension is a heritable condition. We...... compared arterial tonometry measures in a sample of 1564 nonhypertensive Framingham Heart Study third-generation cohort participants (mean age: 38 years; 55% women) whose parents were enrolled in the Framingham Offspring Study. A total of 468, 715, and 381 participants had 0 (referent), 1, and 2 parents...

VARIABLE STIFFNESS HAND PROSTHESIS: A SYSTEMATIC REVIEW

Directory of Open Access Journals (Sweden)

S. Cecilia Tapia-Siles

2017-06-01

Full Text Available Prosthetics is an important field in engineering due to the large number of amputees worldwide and the associated problems such as limited functionality of the state of the art. An important functionality of the human hand is its capability of adjusting the stiffness of the joints depending on the currently performed task. For the development of new technology it is important to understand the limitations of existing resources. As part of our efforts to develop a variable stiffness grasper for developing countries a systematic review was performed covering technology of body powered and myoelectric hand prosthesis. Focus of the review is readiness of prosthetic hands regarding their capability of controlling the stiffness of the end effector. Publications sourced through three different digital libraries were systematically reviewed on the basis of the PRISMA standard. We present a search strategy as well as the PRISMA assessment of the resulting records which covered 321 publications. The records were assessed and the results are presented for the ability of devices to control their joint stiffness. The review indicates that body powered prosthesis are preferred to myoelectric hands due to the reduced cost, the simplicity of use and because of their inherent ability to provide feedback to the user. Stiffness control was identified but has not been fully covered in the current state of the art. In addition we summarise the identified requirements on prosthetic hands as well as related information which can support the development of new prosthetics.

Introduction to computation and modeling for differential equations

CERN Document Server

Edsberg, Lennart

2008-01-01

An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h

Effect of long-term isometric training on core/torso stiffness.

Science.gov (United States)

Lee, Benjamin C Y; McGill, Stuart M

2015-06-01

Although core stiffness enhances athletic performance traits, controversy exists regarding the effectiveness of isometric vs. dynamic core training methods. This study aimed to determine whether long-term changes in stiffness can be trained, and if so, what is the most effective method. Twenty-four healthy male subjects (23 ± 3 years; 1.8 ± 0.06 m; 77.5 ± 10.8 kg) were recruited for passive and active stiffness measurements before and after a 6-week core training intervention. Twelve subjects (22 ± 2 years; 1.8 ± 0.08 m; 78.3 ± 12.3 kg) were considered naive to physical and core exercise. The other 12 subjects (24 ± 3 years; 1.8 ± 0.05 m; 76.8 ± 9.7 kg) were Muay Thai athletes (savvy). A repeated-measures design compared core training methods (isometric vs. dynamic, with a control group) and subject training experience (naive vs. savvy) before and after a 6-week training period. Passive stiffness was assessed on a "frictionless" bending apparatus and active stiffness assessed through a quick release mechanism. Passive stiffness increased after the isometric training protocol. Dynamic training produced a smaller effect, and as expected, there was no change in the control group. Active stiffness did not change in any group. Comparisons between subject and training groups did not reveal any interactions. Thus, an isometric training approach was superior in terms of enhancing core stiffness. This is important since increased core stiffness enhances load bearing ability, arrests painful vertebral micromovements, and enhances ballistic distal limb movement. This may explain the efficacy reported for back and knee injury reduction.

High Order A-stable Continuous General Linear Methods for Solution of Systems of Initial Value Problems in ODEs

Directory of Open Access Journals (Sweden)

Dauda GuliburYAKUBU

2012-12-01

Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.

[Metabolic syndrome and aortic stiffness].

Science.gov (United States)

Simková, A; Bulas, J; Murín, J; Kozlíková, K; Janiga, I

2010-09-01

The metabolic syndrome (MS) is a cluster of risk factors that move the patient into higher level of risk category of cardiovascular disease and the probability of type 2 diabetes mellitus manifestation. Definition of MS is s based on the presence of selected risk factors as: abdominal obesity (lager waist circumpherence), atherogenic dyslipidemia (low value of HDL-cholesterol and increased level of triglycerides), increased fasting blood glucose (or type 2 DM diagnosis), higher blood pressure or antihypertensive therapy. In 2009 there were created harmonizing criteria for MS definition; the condition for assignment of MS is the presence of any 3 criteria of 5 mentioned above. The underlying disorder of MS is an insulin resistance or prediabetes. The patients with MS more frequently have subclinical (preclinical) target organ disease (TOD) which is the early sings of atherosclerosis. Increased aortic stiffness is one of the preclinical diseases and is defined by pathologically increased carotidofemoral pulse wave velocity in aorta (PWV Ao). With the aim to assess the influence of MS on aortic stiffness we examined the group of women with arterial hypertension and MS and compare them with the group of women without MS. The aortic stiffness was examined by Arteriograph--Tensiomed, the equipment working on the oscillometric principle in detection of pulsations of brachial artery. This method determines the global aortic stiffness based on the analysis of the shape of pulse curve of brachial artery. From the cohort of 49 pts 31 had MS, the subgroups did not differ in age or blood pressure level. The mean number of risk factors per person in MS was 3.7 comparing with 1.7 in those without MS. In the MS group there was more frequently abdominal obesity present (87% vs 44%), increased fasting blood glucose (81% vs 22%) and low HDL-cholesterol level. The pulse wave velocity in aorta, PWV Ao, was significantly higher in patients with MS (mean value 10,19 m/s vs 8,96 m

Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System

International Nuclear Information System (INIS)

Wang Qi

2010-01-01

In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations. (general)

Sway‐dependent changes in standing ankle stiffness caused by muscle thixotropy

Science.gov (United States)

Sakanaka, Tania E.; Lakie, Martin

2016-01-01

Key points The passive stiffness of the calf muscles contributes to standing balance, although the properties of muscle tissue are highly labile.We investigated the effect of sway history upon intrinsic ankle stiffness and demonstrated reductions in stiffness of up to 43% during conditions of increased baseline sway.This sway dependence was most apparent when using low amplitude stiffness‐measuring perturbations, and the short‐range stiffness component was smaller during periods of high sway.These characteristics are consistent with the thixotropic properties of the calf muscles causing the observed changes in ankle stiffness.Periods of increased sway impair the passive stabilization of standing, demanding more active neural control of balance. Abstract Quiet standing is achieved through a combination of active and passive mechanisms, consisting of neural control and intrinsic mechanical stiffness of the ankle joint, respectively. The mechanical stiffness is partly determined by the calf muscles. However, the viscoelastic properties of muscle are highly labile, exhibiting a strong dependence on movement history. By measuring the effect of sway history upon ankle stiffness, the present study determines whether this lability has consequences for the passive stabilization of human standing. Ten subjects stood quietly on a rotating platform whose axis was collinear with the ankle joint. Ankle sway was increased by slowly tilting this platform in a random fashion, or decreased by fixing the body to a board. Ankle stiffness was measured by using the same platform to simultaneously apply small, brief perturbations (ankle stiffness by up to 43% compared to the body‐fixed condition. Normal quiet stance was associated with intermediate values. The effect was most apparent when using smaller perturbation amplitudes to measure stiffness (0.1 vs. 0.6 deg). Furthermore, torque responses exhibited a biphasic pattern, consisting of an initial steep rise followed by a

Determination of Ankle and Metatarsophalangeal Stiffness During Walking and Jogging.

Science.gov (United States)

Mager, Fabian; Richards, Jim; Hennies, Malika; Dötzel, Eugen; Chohan, Ambreen; Mbuli, Alex; Capanni, Felix

2018-05-29

Forefoot stiffness has been shown to influence joint biomechanics. However, little or no data exists on metatarsophalangeal stiffness. Twenty-four healthy rearfoot strike runners were recruited from a staff and student population at the University of Central Lancashire. Five repetitions of shod, self-selected speed level walking and jogging were performed. Kinetic and kinematic data were collected using retro-reflective markers placed on the lower limb and foot, to create a three-segment foot model using the Calibrated Anatomical System Technique. Ankle and metatarsophalangeal moments and angles were calculated. Stiffness values were calculated using a linear best fit line of moment versus of angle plots. Paired t-tests were used to compare values between walking and jogging conditions. Significant differences were seen in ankle range of motion (ROM), but not in metatarsophalangeal ROM. Maximum moments were significantly greater in the ankle during jogging, but these were not significantly different at the metatarsophalangeal joint. Average ankle joint stiffness exhibited significantly lower stiffness when walking compared to jogging. However, the metatarsophalangeal joint exhibited significantly greater stiffness when walking compared to jogging. A greater understanding of forefoot stiffness may inform the development of footwear, prosthetic feet and orthotic devices, such as ankle-foot orthoses for walking and sporting activities.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

Science.gov (United States)

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

Dynamically tuned magnetostrictive spring with electrically controlled stiffness

Science.gov (United States)

Scheidler, Justin J.; Asnani, Vivake M.; Dapino, Marcelo J.

2016-03-01

This paper presents the design and testing of an electrically controllable magnetostrictive spring that has a dynamically tunable stiffness (i.e., a magnetostrictive Varispring). The device enables in situ stiffness tuning or stiffness switching for vibration control applications. Using a nonlinear electromechanical transducer model and an analytical solution of linear, mechanically induced magnetic diffusion, Terfenol-D is shown to have a faster rise time to stepped voltage inputs and a significantly higher magnetic diffusion cut-off frequency relative to Galfenol. A Varispring is manufactured using a laminated Terfenol-D rod. Further rise time reductions are achieved by minimizing the rod’s diameter and winding the electromagnet with larger wire. Dynamic tuning of the Varispring’s stiffness is investigated by measuring the Terfenol-D rod’s strain response to dynamic, compressive, axial forces in the presence of sinusoidal or square wave control currents. The Varispring’s rise time is \\lt 1 ms for 1 A current switches. Continuous modulus changes up to 21.9 GPa and 500 Hz and square wave modulus changes (dynamic {{Δ }}E effect) up to 12.3 GPa and 100 Hz are observed. Stiffness tunability and tuning bandwidth can be considerably increased by operating about a more optimal bias stress and improving the control of the electrical input.

Stiff mutant genes of Phycomyces target turgor pressure and wall mechanical properties to regulate elongation growth rate

Directory of Open Access Journals (Sweden)

Joseph K. E. Ortega

2012-05-01

Full Text Available Regulation of cell growth is paramount to all living organisms. In plants, algae and fungi, regulation of expansive growth of cells is required for development and morphogenesis. Also, many sensory responses of stage IVb sporangiophores of Phycomyces blakesleeanus are produced by regulating elongation growth rate (growth responses and differential elongation growth rate (tropic responses. Stiff mutant sporangiophores exhibit diminished tropic responses and are found to be defective in at least four genes; madD, madE, madF and madG. Prior experimental research suggests that the defective genes affect growth regulation, but this was not verified. All the growth of the single-celled stalk of the stage IVb sporangiophore occurs in a short region termed the growth zone. Prior experimental and theoretical research indicates that elongation growth rate of the stage IVb sporangiophore can be regulated by controlling the cell wall mechanical properties within the growth zone and the magnitude of the turgor pressure. A quantitative biophysical model for elongation growth rate is required to elucidate the relationship between wall mechanical properties and turgor pressure during growth regulation. In this study, it is hypothesized that the mechanical properties of the wall within the growth zone of stiff mutant sporangiophores are different compared to wild type. A biophysical equation for elongation growth rate is derived for fungal and plant cells with a growth zone. Two strains of stiff mutants are studied, C149 madD120 (- and C216 geo- (-. Experimental results demonstrate that turgor pressure is larger but irreversible deformation rates of the wall within the growth zone and growth zone length are smaller for stiff mutant sporangiophores compared to wild type. These findings explain the diminished tropic responses of the stiff mutant sporangiophores and suggest that the defective genes affect the amount of wall-building material delivered to the inner

Effects of mechanical properties and geometric conditions on stiffness of Hyperboloid Shallow Shell

Directory of Open Access Journals (Sweden)

Zhao Lihong

2015-01-01

Full Text Available The experiment models based on the hyperboloid shallow shells that represent automobile panel's surface features are established. The effects of material properties and geometric conditions condition on the stiffness of hyperboloid shallow shell are investigated experimentally. The influences of panel thickness and geometric conditions on stiffness are very obvious. Stiffness increases with increasing of the panel thickness, and stiffness doubled as increasing in thickness with 0.1 mm. The effect of thickness on stiffness is far greater than that of blank holding force. The greater the arc height of punch, the greater the stiffness. And stiffness increases nearly by five times with arc height of punch is from 3mm to 9mm. The effect of arc height of punch on stiffness is far greater than that of materials mechanical properties. The stiffness is varied with different panel material properties by the same forming and stiffness test conditions. The decrease of yield strength is beneficial to the panel stiffness. The appropriate choice of materials and forming process condition is important in meeting necessary requirements for the energy-saving, lightweight and reducing wind resistance design in automotive industry.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

Science.gov (United States)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For

Intraventricular filling under increasing left ventricular wall stiffness and heart rates

Science.gov (United States)

Samaee, Milad; Lai, Hong Kuan; Schovanec, Joseph; Santhanakrishnan, Arvind; Nagueh, Sherif

2015-11-01

Heart failure with normal ejection fraction (HFNEF) is a clinical syndrome that is prevalent in over 50% of heart failure patients. HFNEF patients show increased left ventricle (LV) wall stiffness and clinical diagnosis is difficult using ejection fraction (EF) measurements. We hypothesized that filling vortex circulation strength would decrease with increasing LV stiffness irrespective of heart rate (HR). 2D PIV and hemodynamic measurements were acquired on LV physical models of varying wall stiffness under resting and exercise HRs. The LV models were comparatively tested in an in vitro flow circuit consisting of a two-element Windkessel model driven by a piston pump. The stiffer LV models were tested in comparison with the least stiff baseline model without changing pump amplitude, circuit compliance and resistance. Increasing stiffness at resting HR resulted in diminishing cardiac output without lowering EF below 50% as in HFNEF. Increasing HR to 110 bpm in addition to stiffness resulted in lowering EF to less than 50%. The circulation strength of the intraventricular filling vortex diminished with increasing stiffness and HR. The results suggest that filling vortex circulation strength could be potentially used as a surrogate measure of LV stiffness. This research was supported by the Oklahoma Center for Advancement of Science and Technology (HR14-022).

Use of artificial bee colonies algorithm as numerical approximation of differential equations solution

Science.gov (United States)

Fikri, Fariz Fahmi; Nuraini, Nuning

2018-03-01

The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.

The effect of short-term isometric training on core/torso stiffness.

Science.gov (United States)

Lee, Benjamin; McGill, Stuart

2017-09-01

"Core" exercise is a basic part of many physical training regimens with goals ranging from rehabilitation of spine and knee injuries to improving athletic performance. Core stiffness has been proposed to perform several functions including reducing pain by minimising joint micro-movements, and enhancing strength and speed performance. This study probes the links between a training approach and immediate but temporary changes in stiffness. Passive and active stiffness was measured on 24 participants; 12 having little to no experience in core training (inexperienced), and the other 12 being athletes experienced to core training methods; before and after a 15 min bout of isometric core exercises. Passive stiffness was assessed on a "frictionless" bending apparatus and active stiffness assessed via a quick release mechanism. Short-term isometric core training increased passive and active stiffness in most directions for both inexperienced and experienced participants, passive left lateral bend among experienced participants being the exception (P core stiffness, in this case following a single session. This may influence performance and injury resilience for a brief period.

Dynamic Stiffness Transfer Function of an Electromechanical Actuator Using System Identification

Science.gov (United States)

Kim, Sang Hwa; Tahk, Min-Jea

2018-04-01

In the aeroelastic analysis of flight vehicles with electromechanical actuators (EMAs), an accurate prediction of flutter requires dynamic stiffness characteristics of the EMA. The dynamic stiffness transfer function of the EMA with brushless direct current (BLDC) motor can be obtained by conducting complicated mathematical calculations of control algorithms and mechanical/electrical nonlinearities using linearization techniques. Thus, system identification approaches using experimental data, as an alternative, have considerable advantages. However, the test setup for system identification is expensive and complex, and experimental procedures for data collection are time-consuming tasks. To obtain the dynamic stiffness transfer function, this paper proposes a linear system identification method that uses information obtained from a reliable dynamic stiffness model with a control algorithm and nonlinearities. The results of this study show that the system identification procedure is compact, and the transfer function is able to describe the dynamic stiffness characteristics of the EMA. In addition, to verify the validity of the system identification method, the simulation results of the dynamic stiffness transfer function and the dynamic stiffness model were compared with the experimental data for various external loads.

The development of a differential game related to terrorism: Min-Max differential game

Directory of Open Access Journals (Sweden)

Abd El-Monem A. Megahed

2017-07-01

Full Text Available In this work, we study a differential game related to terrorism: Min-Max differential game taking into account the governmental activities such as the education quality, increasing the chances of labor, social justice, religious awareness and security arrangements. A Min-Max differential game between government and terrorist organizations is considered in this study. To obtain the optimal strategy of solving this problem, we study the analytic form of a Min-Max differential game and the governmental activities. Furthermore, a saddle point of a Min-Max differential game is studied.

Martial arts training attenuates arterial stiffness in middle aged adults.

Science.gov (United States)

Douris, Peter C; Ingenito, Teresa; Piccirillo, Barbara; Herbst, Meredith; Petrizzo, John; Cherian, Vincen; McCutchan, Christopher; Burke, Caitlin; Stamatinos, George; Jung, Min-Kyung

2013-09-01

Arterial stiffness increases with age and is related to an increased risk of coronary artery disease. Poor trunk flexibility has been shown to be associated with arterial stiffness in middle-aged subjects. The purpose of our research study was to measure arterial stiffness and flexibility in healthy middle-aged martial artists compared to age and gender matched healthy sedentary controls. Ten martial artists (54.0 ± 2.0 years), who practice Soo Bahk Do (SBD), a Korean martial art, and ten sedentary subjects (54.7 ± 1.8 years) for a total of twenty subjects took part in this cross-sectional study. Arterial stiffness was assessed in all subjects using pulse wave velocity (PWV), a recognized index of arterial stiffness. Flexibility of the trunk and hamstring were also measured. The independent variables were the martial artists and matched sedentary controls. The dependent variables were PWV and flexibility. There were significant differences, between the SBD practitioners and sedentary controls, in PWV (P = 0.004), in trunk flexibility (P= 0.002), and in hamstring length (P= 0.003). The middle-aged martial artists were more flexible in their trunk and hamstrings and had less arterial stiffness compared to the healthy sedentary controls. The flexibility component of martial art training or flexibility exercises in general may be considered as a possible intervention to reduce the effects of aging on arterial stiffness.

Nonlinear Dynamic Buckling of Damaged Composite Cylindrical Shells

Institute of Scientific and Technical Information of China (English)

WANG Tian-lin; TANG Wen-yong; ZHANG Sheng-kun

2007-01-01

Based on the first order shear deformation theory(FSDT), the nonlinear dynamic equations involving transverse shear deformation and initial geometric imperfections were obtained by Hamilton's philosophy. Geometric deformation of the composite cylindrical shell was treated as the initial geometric imperfection in the dynamic equations, which were solved by the semi-analytical method in this paper. Stiffness reduction was employed for the damaged sub-layer, and the equivalent stiffness matrix was obtained for the delaminated area. By circumferential Fourier series expansions for shell displacements and loads and by using Galerkin technique, the nonlinear partial differential equations were transformed to ordinary differential equations which were finally solved by the finite difference method. The buckling was judged from shell responses by B-R criteria, and critical loads were then determined. The effect of the initial geometric deformation on the dynamic response and buckling of composite cylindrical shell was also discussed, as well as the effects of concomitant delamination and sub-layer matrix damages.

A Test Set for stiff Initial Value Problem Solvers in the open source software R: Package deTestSet

NARCIS (Netherlands)

Mazzia, F.; Cash, J.R.; Soetaert, K.

2012-01-01

In this paper we present the R package deTestSet that includes challenging test problems written as ordinary differential equations (ODEs), differential algebraic equations (DAEs) of index up to 3 and implicit differential equations (IDES). In addition it includes 6 new codes to solve initial value

Stiffness Coefficients of Mortise and Tenon Joints used on Wooden Window Profiles

Directory of Open Access Journals (Sweden)

Milan Podlena

2016-04-01

Full Text Available Samples of corner joints of wooden rectangular windows, with widths of 78 and 92 mm, were used to determine the stiffness of tenon and mortise joints. Two series of samples were loaded statically in the angular plane of compression and tension, so that the bending moment could be derived. The objective of the experiment was to determine the existing correlations between the stiffness in maximum strength and the stiffness in the elastic area for both types of tests. After strength tests were carried out, the annual ring width of the samples was measured to determine whether this factor affects the stiffness of the joints. The results showed that there was a relatively strong correlation between the stiffness in the elastic area and the maximum load. A two-factor analysis of variance confirmed that the type of load did not affect the stiffness of the joint, but the type of joint (width does significantly affect the stiffness. Therefore, the width of annual rings was positively correlated with the stiffness of the joints.

Variable stiffness and damping MR isolator

Energy Technology Data Exchange (ETDEWEB)

Zhang, X Z; Wang, X Y; Li, W H; Kostidis, K [University of Wollongong, School of Mechanical, Materials and Mechatronic Engineering, NSW 2522 (Australia)], E-mail: weihuali@uow.edu.au

2009-02-01

This paper presents the development of a magnetorheological (MR) fluid-based variable stiffness and damping isolator for vibration suppressions. The MR fluid isolator used a sole MR control unit to achieve the variable stiffness and damping in stepless and relative large scope. A mathematical model of the isolator was derived, and a prototype of the MR fluid isolator was fabricated and its dynamic behavior was measured in vibration under various applied magnetic fields. The parameters of the model under various magnetic fields were identified and the dynamic performances of isolator were evaluated.

An algorithm for solving initial value problems of third order ordinary ...

African Journals Online (AJOL)

Abstract. We propose an implicit multi-step method for the solution of initial value problems (IVPs) of third order ordinary differential equations (ODE) which does not require reducing the ODE to first order before solving. The development of the method is based on collocation of the differential system and interpolation of the ...

Effect of lumped mass and support stiffness on pipe seismic response

International Nuclear Information System (INIS)

Chang, P.S.Y.

1986-01-01

In performing pipe stress analysis, generic support stiffness values are typically used to predict the response of the piping systems. Consistent design of every support to match the generic stiffness value is difficult. The difference between the actual and generic stiffness may affect the results of pipe stresses and support reactions. The objective of this study is to develop an acceptance criteria for the actual support stiffness and to avoid unnecessary reanalysis. The support mass in the restraint direction and mass within the pipe span can also affect the piping system behavior and this study will discuss this mass effect as well. Added mass and change in support stiffness will cause the piping system to shift frequency

Solving inverse two-point boundary value problems using collage coding

Science.gov (United States)

Kunze, H.; Murdock, S.

2006-08-01

The method of collage coding, with its roots in fractal imaging, is the central tool in a recently established rigorous framework for solving inverse initial value problems for ordinary differential equations (Kunze and Vrscay 1999 Inverse Problems 15 745-70). We extend these ideas to solve the following inverse problem: given a function u(x) on [A, B] (which may be the interpolation of data points), determine a two-point boundary value problem on [A, B] which admits u(x) as a solution as closely as desired. The solution of such inverse problems may be useful in parameter estimation or determination of potential functional forms of the underlying differential equation. We discuss ways to improve results, including the development of a partitioning scheme. Several examples are considered.

Optimization of a variable-stiffness skin for morphing high-lift devices

International Nuclear Information System (INIS)

Thuwis, G A A; Abdalla, M M; Gürdal, Z

2010-01-01

One of the possibilities for the next generation of smart high-lift devices is to use a seamless morphing structure. A passive composite variable-stiffness skin as a solution to the dilemma of designing the structure to have high enough stiffness to withstand aerodynamic loading and low stiffness to enable morphing is proposed. The variable-stiffness skin is achieved by allowing for a spatial fibre angle and skin thickness variation on a morphing high-lift system. The stiffness distribution is tailored to influence the deformation of the structure beneficially. To design a realistic stiffness distribution, it is important to take aerodynamic and actuation loads into account during the optimization. A two-dimensional aero-servo-elastic framework is created for this purpose. Skin optimization is performed using a gradient-based optimizer, where sensitivity information is found through application of the adjoint method. The implementation of the aero-servo-elastic environment is addressed and initial optimization results presented. The results indicate that a variable-stiffness skin increases the design space. Moreover, the importance of taking the change in aerodynamic loads due to morphing skin deformation into account during optimization is demonstrated

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

Science.gov (United States)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

Accurate spring constant calibration for very stiff atomic force microscopy cantilevers

Energy Technology Data Exchange (ETDEWEB)

Grutzik, Scott J.; Zehnder, Alan T. [Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, New York 14853 (United States); Gates, Richard S.; Gerbig, Yvonne B.; Smith, Douglas T.; Cook, Robert F. [Nanomechanical Properties Group, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)

2013-11-15

There are many atomic force microscopy (AFM) applications that rely on quantifying the force between the AFM cantilever tip and the sample. The AFM does not explicitly measure force, however, so in such cases knowledge of the cantilever stiffness is required. In most cases, the forces of interest are very small, thus compliant cantilevers are used. A number of methods have been developed that are well suited to measuring low stiffness values. However, in some cases a cantilever with much greater stiffness is required. Thus, a direct, traceable method for calibrating very stiff (approximately 200 N/m) cantilevers is presented here. The method uses an instrumented and calibrated nanoindenter to determine the stiffness of a reference cantilever. This reference cantilever is then used to measure the stiffness of a number of AFM test cantilevers. This method is shown to have much smaller uncertainty than previously proposed methods. An example application to fracture testing of nanoscale silicon beam specimens is included.

Accurate spring constant calibration for very stiff atomic force microscopy cantilevers

International Nuclear Information System (INIS)

Grutzik, Scott J.; Zehnder, Alan T.; Gates, Richard S.; Gerbig, Yvonne B.; Smith, Douglas T.; Cook, Robert F.

2013-01-01

There are many atomic force microscopy (AFM) applications that rely on quantifying the force between the AFM cantilever tip and the sample. The AFM does not explicitly measure force, however, so in such cases knowledge of the cantilever stiffness is required. In most cases, the forces of interest are very small, thus compliant cantilevers are used. A number of methods have been developed that are well suited to measuring low stiffness values. However, in some cases a cantilever with much greater stiffness is required. Thus, a direct, traceable method for calibrating very stiff (approximately 200 N/m) cantilevers is presented here. The method uses an instrumented and calibrated nanoindenter to determine the stiffness of a reference cantilever. This reference cantilever is then used to measure the stiffness of a number of AFM test cantilevers. This method is shown to have much smaller uncertainty than previously proposed methods. An example application to fracture testing of nanoscale silicon beam specimens is included

A non-penalty recurrent neural network for solving a class of constrained optimization problems.

Science.gov (United States)

Hosseini, Alireza

2016-01-01

In this paper, we explain a methodology to analyze convergence of some differential inclusion-based neural networks for solving nonsmooth optimization problems. For a general differential inclusion, we show that if its right hand-side set valued map satisfies some conditions, then solution trajectory of the differential inclusion converges to optimal solution set of its corresponding in optimization problem. Based on the obtained methodology, we introduce a new recurrent neural network for solving nonsmooth optimization problems. Objective function does not need to be convex on R(n) nor does the new neural network model require any penalty parameter. We compare our new method with some penalty-based and non-penalty based models. Moreover for differentiable cases, we implement circuit diagram of the new neural network. Copyright © 2015 Elsevier Ltd. All rights reserved.

Exchange stiffness of Ca-doped YIG

Science.gov (United States)

Avgin, I.; Huber, D. L.

1994-05-01

An effective medium theory for the zero-temperature exchange stiffness of uncompensated Ca-doped YIG is presented. The theory is based on the assumption that the effect of the Ca impurities is to produce strong, random ferromagnetic interactions between spins on the a and d sublattices. In the simplest version of the theory, a fraction, x, of the ad exchange integrals are large and positive, x being related to the Ca concentration. The stiffness is calculated as function of x for arbitrary perturbed ad exchange integral, Jxad. For Jxad≳(1/5)‖8Jaa+3Jdd‖, with Jaa and Jdd denoting the aa and dd exchange integrals, respectively, there is a critical concentration, Xc, such that when x≳Xc, the stiffness is complex. It is suggested that Xc delineates the region where there are significant departures from colinearity in the ground state of the Fe spins. Extension of the theory to a model where the Ca doping is assumed to generate Fe4+ ions on the tetrahedral sites is discussed. Possible experimental tests of the theory are mentioned.

A New Approach and Solution Technique to Solve Time Fractional Nonlinear Reaction-Diffusion Equations

Directory of Open Access Journals (Sweden)

Inci Cilingir Sungu

2015-01-01

Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.

A multiwell platform for studying stiffness-dependent cell biology.

Science.gov (United States)

Mih, Justin D; Sharif, Asma S; Liu, Fei; Marinkovic, Aleksandar; Symer, Matthew M; Tschumperlin, Daniel J

2011-01-01

Adherent cells are typically cultured on rigid substrates that are orders of magnitude stiffer than their tissue of origin. Here, we describe a method to rapidly fabricate 96 and 384 well platforms for routine screening of cells in tissue-relevant stiffness contexts. Briefly, polyacrylamide (PA) hydrogels are cast in glass-bottom plates, functionalized with collagen, and sterilized for cell culture. The Young's modulus of each substrate can be specified from 0.3 to 55 kPa, with collagen surface density held constant over the stiffness range. Using automated fluorescence microscopy, we captured the morphological variations of 7 cell types cultured across a physiological range of stiffness within a 384 well plate. We performed assays of cell number, proliferation, and apoptosis in 96 wells and resolved distinct profiles of cell growth as a function of stiffness among primary and immortalized cell lines. We found that the stiffness-dependent growth of normal human lung fibroblasts is largely invariant with collagen density, and that differences in their accumulation are amplified by increasing serum concentration. Further, we performed a screen of 18 bioactive small molecules and identified compounds with enhanced or reduced effects on soft versus rigid substrates, including blebbistatin, which abolished the suppression of lung fibroblast growth at 1 kPa. The ability to deploy PA gels in multiwell plates for high throughput analysis of cells in tissue-relevant environments opens new opportunities for the discovery of cellular responses that operate in specific stiffness regimes.

A multiwell platform for studying stiffness-dependent cell biology.

Directory of Open Access Journals (Sweden)

Justin D Mih

Full Text Available Adherent cells are typically cultured on rigid substrates that are orders of magnitude stiffer than their tissue of origin. Here, we describe a method to rapidly fabricate 96 and 384 well platforms for routine screening of cells in tissue-relevant stiffness contexts. Briefly, polyacrylamide (PA hydrogels are cast in glass-bottom plates, functionalized with collagen, and sterilized for cell culture. The Young's modulus of each substrate can be specified from 0.3 to 55 kPa, with collagen surface density held constant over the stiffness range. Using automated fluorescence microscopy, we captured the morphological variations of 7 cell types cultured across a physiological range of stiffness within a 384 well plate. We performed assays of cell number, proliferation, and apoptosis in 96 wells and resolved distinct profiles of cell growth as a function of stiffness among primary and immortalized cell lines. We found that the stiffness-dependent growth of normal human lung fibroblasts is largely invariant with collagen density, and that differences in their accumulation are amplified by increasing serum concentration. Further, we performed a screen of 18 bioactive small molecules and identified compounds with enhanced or reduced effects on soft versus rigid substrates, including blebbistatin, which abolished the suppression of lung fibroblast growth at 1 kPa. The ability to deploy PA gels in multiwell plates for high throughput analysis of cells in tissue-relevant environments opens new opportunities for the discovery of cellular responses that operate in specific stiffness regimes.

Generating random walks and polygons with stiffness in confinement

International Nuclear Information System (INIS)

Diao, Y; Ernst, C; Saarinen, S; Ziegler, U

2015-01-01

The purpose of this paper is to explore ways to generate random walks and polygons in confinement with a bias toward stiffness. Here the stiffness refers to the curvature angle between two consecutive edges along the random walk or polygon. The stiffer the walk (polygon), the smaller this angle on average. Thus random walks and polygons with an elevated stiffness have lower than expected curvatures. The authors introduced and studied several generation algorithms with a stiffness parameter s>0 that regulates the expected curvature angle at a given vertex in which the random walks and polygons are generated one edge at a time using conditional probability density functions. Our generating algorithms also allow the generation of unconfined random walks and polygons with any desired mean curvature angle. In the case of random walks and polygons confined in a sphere of fixed radius, we observe that, as expected, stiff random walks or polygons are more likely to be close to the confinement boundary. The methods developed here require that the random walks and random polygons be rooted at the center of the confinement sphere. (paper)

Optimization of a variable-stiffness skin for morphing high-lift devices

NARCIS (Netherlands)

Thuwis, G.A.A.; Abdalla, M.M.; Gürdal, Z.

2010-01-01

One of the possibilities for the next generation of smart high-lift devices is to use a seamless morphing structure. A passive composite variable-stiffness skin as a solution to the dilemma of designing the structure to have high enough stiffness to withstand aerodynamic loading and low stiffness to

Using Differential Transform Method and Padé Approximant for Solving MHD Flow in a Laminar Liquid Film from a Horizontal Stretching Surface

Directory of Open Access Journals (Sweden)

Mohammad Mehdi Rashidi

2010-01-01

Full Text Available The purpose of this study is to approximate the stream function and temperature distribution of the MHD flow in a laminar liquid film from a horizontal stretching surface. In this paper DTM-Padé method was used which is a combination of differential transform method (DTM and Padé approximant. The DTM solutions are only valid for small values of independent variables. Comparison between the solutions obtained by the DTM and the DTM-Padé with numerical solution (fourth-order Runge–Kutta revealed that the DTM-Padé method is an excellent method for solving MHD boundary-layer equations.

Design of a Variable Stiffness Soft Dexterous Gripper

Science.gov (United States)

Nefti-Meziani, Samia; Davis, Steve

2017-01-01

Abstract This article presents the design of a variable stiffness, soft, three-fingered dexterous gripper. The gripper uses two designs of McKibben muscles. Extensor muscles that increase in length when pressurized are used to form the fingers of the gripper. Contractor muscles that decrease in length when pressurized are then used to apply forces to the fingers through tendons, which cause flexion and extension of the fingers. The two types of muscles are arranged to act antagonistically and this means that by raising the pressure in all of the pneumatic muscles, the stiffness of the system can be increased without a resulting change in finger position. The article presents the design of the gripper, some basic kinematics to describe its function, and then experimental results demonstrating the ability to adjust the bending stiffness of the gripper's fingers. It has been demonstrated that the fingers' bending stiffness can be increased by more than 150%. The article concludes by demonstrating that the fingers can be closed loop position controlled and are able to track step and sinusoidal inputs. PMID:29062630

Bone metabolism and arterial stiffness after renal transplantation.

Science.gov (United States)

Cseprekál, Orsolya; Kis, Eva; Dégi, Arianna A; Kerti, Andrea; Szabó, Attila J; Reusz, György S

2014-01-01

To assess the relationship between bone and vascular disease and its changes over time after renal transplantation. Metabolic bone disease (MBD) is common in chronic kidney disease (CKD) and is associated with cardiovascular (CV) disease. Following transplantation (Tx), improvement in CV disease has been reported; however, data regarding changes in bone disease remain controversial. Bone turnover and arterial stiffness (pulse wave velocity (PWV)) were assessed in 47 Tx patients (38 (3-191) months after Tx). Bone alkaline phosphatase (BALP), osteocalcin (OC) and beta-crosslaps were significantly higher in Tx patients, and decreased significantly after one year. There was a negative correlation between BALP, OC and steroid administered (r = -0.35; r = -0.36 respectively). PWV increased in the Tx group (1.15 SD). In patients with a follow up of bone turnover and arterial stiffness are present following kidney transplantation. While bone turnover decreases with time, arterial stiffness correlates initially with bone turnover, after which the influence of cholesterol becomes significant. Non-invasive estimation of bone metabolism and arterial stiffness may help to assess CKD-MBD following renal transplantation.

Quarter-Sweep Iteration Concept on Conjugate Gradient Normal Residual Method via Second Order Quadrature - Finite Difference Schemes for Solving Fredholm Integro-Differential Equations

International Nuclear Information System (INIS)

Aruchunan, E.

2015-01-01

In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods. (author)

Identification of a parametric, discrete-time model of ankle stiffness.

Science.gov (United States)

Guarin, Diego L; Jalaleddini, Kian; Kearney, Robert E

2013-01-01

Dynamic ankle joint stiffness defines the relationship between the position of the ankle and the torque acting about it and can be separated into intrinsic and reflex components. Under stationary conditions, intrinsic stiffness can described by a linear second order system while reflex stiffness is described by Hammerstein system whose input is delayed velocity. Given that reflex and intrinsic torque cannot be measured separately, there has been much interest in the development of system identification techniques to separate them analytically. To date, most methods have been nonparametric and as a result there is no direct link between the estimated parameters and those of the stiffness model. This paper presents a novel algorithm for identification of a discrete-time model of ankle stiffness. Through simulations we show that the algorithm gives unbiased results even in the presence of large, non-white noise. Application of the method to experimental data demonstrates that it produces results consistent with previous findings.

Extension of elastic stiffness formula for leaf type holddown spring assembly

Energy Technology Data Exchange (ETDEWEB)

Song, Kee Nam; Kang, Heung Seok; Yoon, Kyung Ho; Kim, Hyung Kyu [Korea Atomic Energy Research Institute, Taejon (Korea)

1998-09-01

Based on the Euler beam theory and the strain energy method, an elastic stiffness formula of the holddown spring assembly consisting of several leaves was previously derived. The formula was known to be useful to estimate the elastic stiffness of the holddown spring assembly only with the geometric data and the material properties of the leaf. Recently, it was reported that the elastic stiffness from the formula deviated much from the test results as the number of leaves was increased. In this study, in order to resolve such an increasing deviation as the increasing number of leaves, the formula has been extended to be able to consider normal forces and friction forces acting on interfaces between the leaves. The elastic stiffness analysis on specimens of leaf type holddown springs has been carried out using the extended formula and the analysis results are compared with the test results. As a result of comparisons, it is found that the extended formula is able to evaluate the elastic stiffness of the holddown spring assembly within an error range of 10%, irrespective of the number of leaves. In addition, it is found that the effect of shear forces and axial forces on the elastic stiffness of the holddown spring assembly is only below 0.2% of the elastic stiffness, and therefore the greatest portion of the elastic stiffness of the holddown spring assembly is attributed to the bending moment. (author). 13 refs., 10 figs., 12 tabs.

Dynamic Functional Stiffness Index of the Ankle Joint During Daily Living.

Science.gov (United States)

Argunsah Bayram, Hande; Bayram, Mehmed B

2018-03-30

Exploring ankle joint physiologic functional stiffness is crucial for improving the design of prosthetic feet that aim to mimic normal gait. We hypothesized that ankle joint stiffness would vary among the different activities of daily living and that the magnitude of the stiffness would indicate the degree of energy storage element sufficiency in terms of harvesting and returning energy. We examined sagittal plane ankle moment versus flexion angle curves from 12 healthy subjects during the daily activities. The slopes of these curves were assessed to find the calculated stiffness during the peak energy return and harvest phases. For the energy return and harvest phases, stiffness varied from 0.016 to 0.283 Nm/kg° and 0.025 and 0.858 Nm/kg°, respectively. The optimum stiffness during the energy return phase was 0.111 ± 0.117 Nm/kg° and during the energy harvest phase was 0.234 ± 0.327 Nm/kg°. Ankle joint stiffness varied significantly during the activities of daily living, indicating that an energy storage unit with a constant stiffness would not be sufficient in providing energy regenerative gait during all activities. The present study was directed toward the development of a complete data set to determine the torque-angle properties of the ankle joint to facilitate a better design process. Copyright © 2017 The American College of Foot and Ankle Surgeons. Published by Elsevier Inc. All rights reserved.

Calculus & ordinary differential equations

CERN Document Server

Pearson, David

1995-01-01

Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.

Introduction to partial differential equations

CERN Document Server

Greenspan, Donald

2000-01-01

Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

Uncertain differential equations

CERN Document Server

Yao, Kai

2016-01-01

This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

Parametric study of roof diaphragm stiffness requirements

International Nuclear Information System (INIS)

Jones, W.D.; Tenbus, M.A.

1991-01-01

A common assumption made in performing a dynamic seismic analysis for a building is that the roof/floor system is open-quotes rigidclose quotes. This assumption would appear to be reasonable for many of the structures found in nuclear power plants, since many of these structures are constructed of heavily reinforced concrete having floor/roof slabs at least two feet in thickness, and meet the code requirements for structural detailing for seismic design. The roofs of many Department of Energy (DOE) buildings at the Oak Ridge Y-12 Plant in Oak Ridge, Tennessee, have roofs constructed of either metal, precast concrete or gypsum plank deck overlaid with rigid insulation, tar and gravel. In performing natural phenomena hazard assessments for one such facility, it was assumed that the existing roof performed first as a flexible diaphragm (zero stiffness) and then, rigid (infinitely stiff). For the flexible diaphragm model it was determined that the building began to experience significant damage around 0.09 g's. For the rigid diaphragm model it was determined that no significant damage was observed below 0.20 g's. A Conceptual Design Report has been prepared for upgrading/replacing the roof of this building. The question that needed to be answered here was, open-quotes How stiff should the new roof diaphragm be in order to satisfy the rigid diaphragm assumption and, yet, be cost effective?close quotes. This paper presents a parametric study of a very simple structural system to show that the design of roof diaphragms needs to consider both strength and stiffness (frequency) requirements. This paper shows how the stiffness of a roof system affects the seismically induced loads in the lateral, vertical load resisting elements of a building and provides guidance in determining how open-quotes rigidclose quotes a roof system should be in order to accomplish a cost effective design

Comparative study of diastolic filling under varying left ventricular wall stiffness

Science.gov (United States)

Mekala, Pritam; Santhanakrishnan, Arvind

2014-11-01

Pathological remodeling of the human cardiac left ventricle (LV) is observed in hypertensive heart failure as a result of pressure overload. Myocardial stiffening occurs in these patients prior to chronic maladaptive changes, resulting in increased LV wall stiffness. The goal of this study was to investigate the change in intraventricular filling fluid dynamics inside a physical model of the LV as a function of wall stiffness. Three LV models of varying wall stiffness were incorporated into an in vitro flow circuit driven by a programmable piston pump. Windkessel elements were used to tune the inflow and systemic pressure in the model with least stiffness to match healthy conditions. Models with stiffer walls were comparatively tested maintaining circuit compliance, resistance and pump amplitude constant. 2D phase-locked PIV measurements along the central plane showed that with increase in wall stiffness, the peak velocity and cardiac output inside the LV decreased. Further, inflow vortex ring propagation toward the LV apex was reduced with increasing stiffness. The above findings indicate the importance of considering LV wall relaxation characteristics in pathological studies of filling fluid dynamics.

Leg stiffness during phases of countermovement and take-off in vertical jump.

Science.gov (United States)

Struzik, Artur; Zawadzki, Jerzy

2013-01-01

With respect to cyclic movements such as human gait, running or hopping, leg stiffness is a little variable parameter. The aim of this study was to investigate changes in leg stiffness during the phase of countermovement and take-off when performing a single maximum counter-movement jump. Kistler force plates and a BTS SMART system for comprehensive motion analysis were employed in the study. The study covered a group of 12 athletes from university basketball teams. Leg stiffness was calculated in those parts of countermovement and take-off phases where its level is relatively constant and the relationship F(Δl) is similar to linear one. Mean total stiffness (±SD) in both legs in the countermovement phase amounted to 6.5 ± 1.5 kN/m, whereas during the take-off phase this value was 6.9 ± 1 kN/m. No statistically significant differences were found between leg stiffness during the countermovement phase and takeoff phase in the study group at the level of significance set at α = 0.05. This suggests that the leg stiffness in phase of countermovement and phase of take-off are much similar to each other, despite different function of both phases. Similar to cyclic movements, leg stiffness turned out relatively constant when performing a single vertical jump. There are also reported statistically significant correlations between body mass, body height, length of lower limbs and leg stiffness. The stiffness analysed by the authors should be understood as quasi-stiffness because the measurements of ΔF(Δl) were made during transient states where inertia and dumping forces are likely to affect the final result.

Flexural Stiffness of Myosin Va Subdomains as Measured from Tethered Particle Motion

Science.gov (United States)

Michalek, Arthur J.; Kennedy, Guy G.; Warshaw, David M.; Ali, M. Yusuf

2015-01-01

Myosin Va (MyoVa) is a processive molecular motor involved in intracellular cargo transport on the actin cytoskeleton. The motor's processivity and ability to navigate actin intersections are believed to be governed by the stiffness of various parts of the motor's structure. Specifically, changes in calcium may regulate motor processivity by altering the motor's lever arm stiffness and thus its interhead communication. In order to measure the flexural stiffness of MyoVa subdomains, we use tethered particle microscopy, which relates the Brownian motion of fluorescent quantum dots, which are attached to various single- and double-headed MyoVa constructs bound to actin in rigor, to the motor's flexural stiffness. Based on these measurements, the MyoVa lever arm and coiled-coil rod domain have comparable flexural stiffness (0.034 pN/nm). Upon addition of calcium, the lever arm stiffness is reduced 40% as a result of calmodulins potentially dissociating from the lever arm. In addition, the flexural stiffness of the full-length MyoVa construct is an order of magnitude less stiff than both a single lever arm and the coiled-coil rod. This suggests that the MyoVa lever arm-rod junction provides a flexible hinge that would allow the motor to maneuver cargo through the complex intracellular actin network. PMID:26770194

Technical Validation of ARTSENS–An Image Free Device for Evaluation of Vascular Stiffness

Science.gov (United States)

Radhakrishnan, Ravikumar; Kusmakar, Shitanshu; Thrivikraman, Arya Sree; Sivaprakasam, Mohanasankar

2015-01-01

Vascular stiffness is an indicator of cardiovascular health, with carotid artery stiffness having established correlation to coronary heart disease and utility in cardiovascular diagnosis and screening. State of art equipment for stiffness evaluation are expensive, require expertise to operate and not amenable for field deployment. In this context, we developed ARTerial Stiffness Evaluation for Noninvasive Screening (ARTSENS), a device for image free, noninvasive, automated evaluation of vascular stiffness amenable for field use. ARTSENS has a frugal hardware design, utilizing a single ultrasound transducer to interrogate the carotid artery, integrated with robust algorithms that extract arterial dimensions and compute clinically accepted measures of arterial stiffness. The ability of ARTSENS to measure vascular stiffness in vivo was validated by performing measurements on 125 subjects. The accuracy of results was verified with the state-of-the-art ultrasound imaging-based echo-tracking system. The relation between arterial stiffness measurements performed in sitting posture for ARTSENS measurement and sitting/supine postures for imaging system was also investigated to examine feasibility of performing ARTSENS measurements in the sitting posture for field deployment. This paper verified the feasibility of the novel ARTSENS device in performing accurate in vivo measurements of arterial stiffness. As a portable device that performs automated measurement of carotid artery stiffness with minimal operator input, ARTSENS has strong potential for use in large-scale screening. PMID:27170892

Superfluid phase stiffness in electron doped superconducting Gd-123

Science.gov (United States)

Das, P.; Ghosh, Ajay Kumar

2018-05-01

Current-voltage characteristics of Ce substituted Gd-123 superconductor exhibits nonlinearity below a certain temperature below the critical temperature. An exponent is extracted using the nonlinearity of current-voltage relation. Superfluid phase stiffness has been studied as a function of temperature following the Ambegaokar-Halperin-Nelson-Siggia (AHNS) theory. Phase stiffness of the superfluid below the superconducting transition is found to be sensitive to the change in the carrier concentration in superconducting system. There may be a crucial electron density which affects superfluid stiffness strongly. Electron doping is found to be effective even if the coupling of the superconducting planes is changed.

Variable stiffness corrugated composite structure with shape memory polymer for morphing skin applications

Science.gov (United States)

Gong, Xiaobo; Liu, Liwu; Scarpa, Fabrizio; Leng, Jinsong; Liu, Yanju

2017-03-01

This work presents a variable stiffness corrugated structure based on a shape memory polymer (SMP) composite with corrugated laminates as reinforcement that shows smooth aerodynamic surface, extreme mechanical anisotropy and variable stiffness for potential morphing skin applications. The smart composite corrugated structure shows a low in-plane stiffness to minimize the actuation energy, but also possess high out-of-plane stiffness to transfer the aerodynamic pressure load. The skin provides an external smooth aerodynamic surface because of the one-sided filling with the SMP. Due to variable stiffness of the shape memory polymer the morphing skin exhibits a variable stiffness with a change of temperature, which can help the skin adjust its stiffness according different service environments and also lock the temporary shape without external force. Analytical models related to the transverse and bending stiffness are derived and validated using finite element techniques. The stiffness of the morphing skin is further investigated by performing a parametric analysis against the geometry of the corrugation and various sets of SMP fillers. The theoretical and numerical models show a good agreement and demonstrate the potential of this morphing skin concept for morphing aircraft applications. We also perform a feasibility study of the use of this morphing skin in a variable camber morphing wing baseline. The results show that the morphing skin concept exhibits sufficient bending stiffness to withstand the aerodynamic load at low speed (less than 0.3 Ma), while demonstrating a large transverse stiffness variation (up to 191 times) that helps to create a maximum mechanical efficiency of the structure under varying external conditions.

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

Directory of Open Access Journals (Sweden)

Hassan Saberi Nik

2014-01-01

Full Text Available We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

Teaching Differentials in Thermodynamics Using Spatial Visualization

Science.gov (United States)

Wang, Chih-Yueh; Hou, Ching-Han

2012-01-01

The greatest difficulty that is encountered by students in thermodynamics classes is to find relationships between variables and to solve a total differential equation that relates one thermodynamic state variable to two mutually independent state variables. Rules of differentiation, including the total differential and the cyclic rule, are…

Problem-Solving Test: The Mechanism of Protein Synthesis

Science.gov (United States)

Szeberenyi, Jozsef

2009-01-01

Terms to be familiar with before you start to solve the test: protein synthesis, ribosomes, amino acids, peptides, peptide bond, polypeptide chain, N- and C-terminus, hemoglobin, [alpha]- and [beta]-globin chains, radioactive labeling, [[to the third power]H] and [[to the fourteenth power]C]leucine, cytosol, differential centrifugation, density…

Water retention properties of stiff silt

Directory of Open Access Journals (Sweden)

Barbara Likar

2017-06-01

Full Text Available Recent research into the behaviour of soils has shown that it is in fact much more complex than can be described by the mechanics of saturated soils. Nowadays the trend of investigations has shifted towards the unsaturated state. Despite the signifiant progress that has been made so far, there are still a lot of unanswered questions related to the behaviour of unsaturated soils. For this reason, in the fild of geotechnics some new concepts are developed, which include the study of soil suction. Most research into soil suction has involved clayey and silty material, whereas up until recently no data have been available about measurements in very stiff preconsolidated sandy silt. Very stiff preconsolidated sandy silt is typical of the Krško Basin, where it is planned that some very important geotechnical structures will be built, so that knowledge about the behaviour of such soils at increased or decreased water content is essential. Several different methods can be used for soil suction measurements. In the paper the results of measurements carried out on very stiff preconsolidated sandy silt in a Bishop - Wesley double-walled triaxial cell are presented and compared with the results of soil suction measurements performed by means of a potentiometer (WP4C. All the measurement results were evaluated taking into account already known results given in the literature, using the three most commonly used mathematical models. Until now a lot of papers dealing with suction measurements in normal consolidated and preconsolidated clay have been published. Measurements on very stiff preconsolidated sandy silt, as presented in this paper were not supported before.

Modelling, simulation and experiment of the spherical flexible joint stiffness

Directory of Open Access Journals (Sweden)

S. Li

2018-02-01

Full Text Available The spherical flexible joint is extensively used in engineering. It is designed to provide flexibility in rotation while bearing vertical compression load. The linear rotational stiffness of the flexible joint is formulated. The rotational stiffness of the bonded rubber layer is related to inner radius, thickness and two edge angles. FEM is used to verify the analytical solution and analyze the stiffness. The Mooney–Rivlin, Neo Hooke and Yeoh constitutive models are used in the simulation. The experiment is taken to obtain the material coefficient and validate the analytical and FEM results. The Yeoh model can reflect the deformation trend more accurately, but the error in the nearly linear district is bigger than the Mooney–Rivlin model. The Mooney–Rivlin model can fit the test result very well and the analytical solution can also be used when the rubber deformation in the flexible joint is small. The increase of Poisson's ratio of the rubber layers will enhance the vertical compression stiffness but barely have effect on the rotational stiffness.

A METHOD OF DETERMINING THE COORDINATES OF THE STIFFNESS CENTER AND THE STIFFNESS PRINCIPAL AXIS OF THE VIBRATING SYSTEM WITH DAMPING

OpenAIRE

Dang Xuan Truong; Tran Duc Chinh

2014-01-01

The report presents a methodology to determine the directions of the stiffness principal axis (in this case subject to the linear displacement and forced rotation angle) of a solid object interact with the surrounding environment by resilient bearing supports. The results also show that determining the coordinates of the stiffness center in the vibrating system with damping factors is necessary in our research.

Dynamic stiffness of suction caissons

DEFF Research Database (Denmark)

Ibsen, Lars Bo; Liingaard, Morten; Andersen, Lars

This report concerns the dynamic soil-structure interaction of steel suction caissons applied as foundations for offshore wind turbines. An emphasis is put on torsional vibrations and coupled sliding/rocking motion, and the influence of the foundation geometry and the properties of the surrounding...... soil is examined. The soil is simplified as a homogenous linear viscoelastic material and the dynamic stiffness of the suction caisson is expressed in terms of dimensionless frequency-dependent coefficients corresponding to the different degrees of freedom. The dynamic stiffness coefficients...... for the skirted foundation are evaluated by means of a three-dimensional coupled boundary element/finite element model. Comparisons with known analytical and numerical solutions indicate that the static and dynamic behaviour of the foundation are predicted accurately with the applied model. The analysis has been...

Finding trap stiffness of optical tweezers using digital filters.

Science.gov (United States)

Almendarez-Rangel, Pedro; Morales-Cruzado, Beatriz; Sarmiento-Gómez, Erick; Pérez-Gutiérrez, Francisco G

2018-02-01

Obtaining trap stiffness and calibration of the position detection system is the basis of a force measurement using optical tweezers. Both calibration quantities can be calculated using several experimental methods available in the literature. In most cases, stiffness determination and detection system calibration are performed separately, often requiring procedures in very different conditions, and thus confidence of calibration methods is not assured due to possible changes in the environment. In this work, a new method to simultaneously obtain both the detection system calibration and trap stiffness is presented. The method is based on the calculation of the power spectral density of positions through digital filters to obtain the harmonic contributions of the position signal. This method has the advantage of calculating both trap stiffness and photodetector calibration factor from the same dataset in situ. It also provides a direct method to avoid unwanted frequencies that could greatly affect calibration procedure, such as electric noise, for example.

Potential Relationship between Passive Plantar Flexor Stiffness and Running Performance.

Science.gov (United States)

Ueno, Hiromasa; Suga, Tadashi; Takao, Kenji; Tanaka, Takahiro; Misaki, Jun; Miyake, Yuto; Nagano, Akinori; Isaka, Tadao

2018-02-01

The present study aimed to determine the relationship between passive stiffness of the plantar flexors and running performance in endurance runners. Forty-eight well-trained male endurance runners and 24 untrained male control subjects participated in this study. Plantar flexor stiffness during passive dorsiflexion was calculated from the slope of the linear portion of the torque-angle curve. Of the endurance runners included in the present study, running economy in 28 endurance runners was evaluated by measuring energy cost during three 4-min trials (14, 16, and 18 km/h) of submaximal treadmill running. Passive stiffness of the plantar flexors was significantly higher in endurance runners than in untrained subjects. Moreover, passive plantar flexor stiffness in endurance runners was significantly correlated with a personal best 5000-m race time. Furthermore, passive plantar flexor stiffness in endurance runners was significantly correlated with energy cost during submaximal running at 16 km/h and 18 km/h, and a trend towards such significance was observed at 14 km/h. The present findings suggest that stiffer plantar flexors may help achieve better running performance, with greater running economy, in endurance runners. Therefore, in the clinical setting, passive stiffness of the plantar flexors may be a potential parameter for assessing running performance. © Georg Thieme Verlag KG Stuttgart · New York.

Social Problem-Solving Skills of Children in Terms of Maternal Acceptance-Rejection Levels

Science.gov (United States)

Tepeli, Kezban; Yilmaz, Elif

2013-01-01

This study was conducted to find an answer to the question of "Do social problem-solving skills of 5-6 years old children differentiate depending on the levels of maternal acceptance rejection?" The participants of the study included 359 5-6 years old children and their mothers. Wally Social Problem-Solving Test and PARQ (Parental…

An introduction to neural network methods for differential equations

CERN Document Server

Yadav, Neha; Kumar, Manoj

2015-01-01

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed...

Methods of solving nonstandard problems

CERN Document Server

Grigorieva, Ellina

2015-01-01

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.   It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad. Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions.  The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem.  Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems.   Over 360 problems are included with hints, ...

Review of current and coming attractions

Energy Technology Data Exchange (ETDEWEB)

Byrne, G.D.; Hindmarsh, A.C.

1987-05-01

Stiff ordinary differential equation (ODEs) can now be solved more or less routinely. This review is intended for the user who is interested in learning how to solve these systems of equations. Consequently, this review explains what stiff ODEs are and where they arise. It tells what is expected of the solftware and sketches how it works. So, several tried and true, as well as experimental, numerical methods are outlined. Perhaps the most salient feature is a set of examples that has been compiled during the last 15 years. These examples include several prototypical problems. The problems are deliberately tractable in size, yet display features of much larger problems in science and engineering. In each case, the choice of the software package, the ODE solver, is given. These choices are based on the author's combined experience and take into account problem structure. This then is a brief handbook which could be used to learn or to teach the pragmatics of numerically solving stiff ODEs. This work should be useful to line scientists, scientific computing managers, and to students. copyright 1987 Academic Press, Inc.

Arterial stiffness in normotensive and hypertensive subjects: Frequency in community pharmacies.

Science.gov (United States)

Rodilla Sala, Enrique; Adell Alegre, Manuel; Giner Galvañ, Vicente; Perseguer Torregrosa, Zeneida; Pascual Izuel, Jose Maria; Climent Catalá, María Teresa

2017-12-07

Arterial stiffness (AS) is a well-recognized target organ lesion. This study aims to determine: 1) the frequency of AS in community pharmacies; 2) if stiffened subjects identified by brachial oscillometry have more CV risk factors than normal subjects, and 3) the dependence of stiffness on using either age-adjusted values or a fixed threshold. Observational, cross-sectional study in 32 community pharmacies of the Valencia Community, between November/2015 and April/2016. Stiffness was as pulse wave velocity (PWV) measured with a semi-automatic, validated device (Mobil-O-Graph ® , IEM), followed by a 10-item questionnaire. Mean age of the 1,427 consecutive recruited patients was 56.6 years. Overall proportion of patients with AS was 17.4% with age-adjusted PWV (9.4% in normotensives, 28.3% in hypertensives). Multivariate logistic regression showed independent association of stiffness in normotensives with male gender, obesity, higher pulse pressure and heart rate, in hypertensives, with higher pulse pressure and lower age. AS was globally found in 20.5% of subjects, defining stiffness by PWV>10m/s (6.2% in normotensives, 40.2% in hypertensives). It was associated with higher age and pulse pressure in both groups. Concordance in classifying stiffness was 74.6%. Frequency of AS varied between 17.4-20.5%. Age-adjusted stiffness is associated in normotensives with male gender, pulse pressure, obesity and heart rate, in hypertensives with pulse pressure and inversely to age. Stiffness by 10m/s is determined by higher pulse pressure and higher age. Both definitions of PWV are not interchangeable. Copyright © 2017 Elsevier España, S.L.U. All rights reserved.

Modified Differential Transform Method for Two Singular Boundary Values Problems

Directory of Open Access Journals (Sweden)

Yinwei Lin

2014-01-01

Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

Experimental study on vertical static stiffnesses of polycal wire rope isolators

Science.gov (United States)

Balaji, P. S.; Moussa, Leblouba; Khandoker, Noman; Yuk Shyh, Ting; Rahman, M. E.; Hieng Ho, Lau

2017-07-01

Wire rope isolator is one of the most effective isolation system that can be used to attenuate the vibration disturbances and shocks during the operation of machineries. This paper presents the results of investigation on static elastic stiffnesses (both in tension and in compression) of Polycal Wire Rope Isolator (PWRI) under quasi-static monotonic loading conditions. It also studied effect of variations in height and width of PWRI on its static stiffnesses. Suitable experimental setup was designed and manufactured to meet the test conditions. The results show that their elastic stiffnesses for both tension and compression loading conditions are highly influenced by their geometric dimensions. It is found that their compressive stiffness reduced by 55% for an increment of 20% in their height to width ratio. Therefore, the stiffness of PWRI can be fine-tuned by controlling their dimensions according to the requirements of the application.

A METHOD OF DETERMINING THE COORDINATES OF THE STIFFNESS CENTER AND THE STIFFNESS PRINCIPAL AXIS OF THE VIBRATING SYSTEM WITH DAMPING

Directory of Open Access Journals (Sweden)

Dang Xuan Truong

2014-12-01

Full Text Available The report presents a methodology to determine the directions of the stiffness principal axis (in this case subject to the linear displacement and forced rotation angle of a solid object interact with the surrounding environment by resilient bearing supports. The results also show that determining the coordinates of the stiffness center in the vibrating system with damping factors is necessary in our research.

Acute changes in arterial stiffness following exercise in people with metabolic syndrome.

Science.gov (United States)

Radhakrishnan, Jeyasundar; Swaminathan, Narasimman; Pereira, Natasha M; Henderson, Keiran; Brodie, David A

This study aims to examine the changes in arterial stiffness immediately following sub-maximal exercise in people with metabolic syndrome. Ninety-four adult participants (19-80 years) with metabolic syndrome gave written consent and were measured for arterial stiffness using a SphygmoCor (SCOR-PVx, Version 8.0, Atcor Medical Private Ltd, USA) immediately before and within 5-10min after an incremental shuttle walk test. The arterial stiffness measures used were pulse wave velocity (PWV), aortic pulse pressure (PP), augmentation pressure, augmentation index (AI), subendocardial viability ratio (SEVR) and ejection duration (ED). There was a significant increase (pexercise. Exercise capacity had a strong inverse correlation with arterial stiffness and age (pExercise capacity is inversely related to arterial stiffness and age in people with metabolic syndrome. Exercise induced changes in arterial stiffness measured using pulse wave analysis is an important tool that provides further evidence in studying cardiovascular risk in metabolic syndrome. Copyright © 2016 Diabetes India. Published by Elsevier Ltd. All rights reserved.

Spatially varying small-strain stiffness in soils subjected to K0 loading

KAUST Repository

Kim, Hyun-Ki; Santamarina, Carlos

2017-01-01

Grain-scale characteristics and formation history determine spatial variability in granular masses. We investigate the effect of spatially varying stiffness on the load-deformation response under zero-lateral strain conditions using numerical simulations of correlated random fields, where the granular medium is represented by a non-linear stress-dependent meso-scale model. Results show that stiffness heterogeneity results in higher global compressibility as compared to the homogeneous medium with the same arithmetic mean stiffness. Furthermore, the non-homogeneous stress field that develops inside the granular mass is characterized by focused load transfer along columnar regions, higher stress anisotropy and lower horizontal-to-vertical stress ratio K0 than in a granular medium of homogenous stiffness. As the applied stress increases, the inherent stress-dependent response of the granular material leads to a more homogenous stress field. While greater variance in stiffness causes lower global stiffness, a longer correlation length results in greater variance in global mechanical response among multiple realizations.

Spatially varying small-strain stiffness in soils subjected to K0 loading

KAUST Repository

Kim, Hyun-Ki

2017-08-08

Grain-scale characteristics and formation history determine spatial variability in granular masses. We investigate the effect of spatially varying stiffness on the load-deformation response under zero-lateral strain conditions using numerical simulations of correlated random fields, where the granular medium is represented by a non-linear stress-dependent meso-scale model. Results show that stiffness heterogeneity results in higher global compressibility as compared to the homogeneous medium with the same arithmetic mean stiffness. Furthermore, the non-homogeneous stress field that develops inside the granular mass is characterized by focused load transfer along columnar regions, higher stress anisotropy and lower horizontal-to-vertical stress ratio K0 than in a granular medium of homogenous stiffness. As the applied stress increases, the inherent stress-dependent response of the granular material leads to a more homogenous stress field. While greater variance in stiffness causes lower global stiffness, a longer correlation length results in greater variance in global mechanical response among multiple realizations.

Parametric instability of spinning elastic rings excited by fluctuating space-fixed stiffnesses

Science.gov (United States)

Liu, Chunguang; Cooley, Christopher G.; Parker, Robert G.

2017-07-01

This study investigates the vibration of rotating elastic rings that are dynamically excited by an arbitrary number of space-fixed discrete stiffnesses with periodically fluctuating stiffnesses. The rotating, elastic ring is modeled using thin-ring theory with radial and tangential deformations. Primary and combination instability regions are determined in closed-form using the method of multiple scales. The ratio of peak-to-peak fluctuation to average discrete stiffness is used as the perturbation parameter, so the resulting perturbation analysis is not limited to small mean values of discrete stiffnesses. The natural frequencies and vibration modes are determined by discretizing the governing equations using Galerkin's method. Results are demonstrated for compliant gear applications. The perturbation results are validated by direct numerical integration of the equations of motion and Floquet theory. The bandwidths of the instability regions correlate with the fractional strain energy stored in the discrete stiffnesses. For rings with multiple discrete stiffnesses, the phase differences between them can eliminate large amplitude response under certain conditions.

Arterial stiffness

Directory of Open Access Journals (Sweden)

Ursula Quinn

2012-09-01

Full Text Available Measurements of biomechanical properties of arteries have become an important surrogate outcome used in epidemiological and interventional cardiovascular research. Structural and functional differences of vessels in the arterial tree result in a dampening of pulsatility and smoothing of blood flow as it progresses to capillary level. A loss of arterial elastic properties results a range of linked pathophysiological changes within the circulation including increased pulse pressure, left ventricular hypertrophy, subendocardial ischaemia, vessel endothelial dysfunction and cardiac fibrosis. With increased arterial stiffness, the microvasculature of brain and kidneys are exposed to wider pressure fluctuations and may lead to increased risk of stroke and renal failure. Stiffening of the aorta, as measured by the gold-standard technique of aortic Pulse Wave Velocity (aPWV, is independently associated with adverse cardiovascular outcomes across many different patient groups and in the general population. Therefore, use of aPWV has been proposed for early detection of vascular damage and individual cardiovascular risk evaluation and it seems certain that measurement of arterial stiffness will become increasingly important in future clinical care. In this review we will consider some of the pathophysiological processes that result from arterial stiffening, how it is measured and factors that may drive it as well as potential avenues for therapy. In the face of an ageing population where mortality from atheromatous cardiovascular disease is falling, pathology associated with arterial stiffening will assume ever greater importance. Therefore, understanding these concepts for all clinicians involved in care of patients with cardiovascular disease will become vital.

Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

KAUST Repository

Alzahrani, Hasnaa H.

2016-01-01

A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge

The most precise computations using Euler's method in standard floating-point arithmetic applied to modelling of biological systems.

Science.gov (United States)

Kalinina, Elizabeth A

2013-08-01

The explicit Euler's method is known to be very easy and effective in implementation for many applications. This article extends results previously obtained for the systems of linear differential equations with constant coefficients to arbitrary systems of ordinary differential equations. Optimal (providing minimum total error) step size is calculated at each step of Euler's method. Several examples of solving stiff systems are included. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Increase in Leg Stiffness Reduces Joint Work During Backpack Carriage Running at Slow Velocities.

Science.gov (United States)

Liew, Bernard; Netto, Kevin; Morris, Susan

2017-10-01

Optimal tuning of leg stiffness has been associated with better running economy. Running with a load is energetically expensive, which could have a significant impact on athletic performance where backpack carriage is involved. The purpose of this study was to investigate the impact of load magnitude and velocity on leg stiffness. We also explored the relationship between leg stiffness and running joint work. Thirty-one healthy participants ran overground at 3 velocities (3.0, 4.0, 5.0 m·s -1 ), whilst carrying 3 load magnitudes (0%, 10%, 20% weight). Leg stiffness was derived using the direct kinetic-kinematic method. Joint work data was previously reported in a separate study. Linear models were used to establish relationships between leg stiffness and load magnitude, velocity, and joint work. Our results found that leg stiffness did not increase with load magnitude. Increased leg stiffness was associated with reduced total joint work at 3.0 m·s -1 , but not at faster velocities. The association between leg stiffness and joint work at slower velocities could be due to an optimal covariation between skeletal and muscular components of leg stiffness, and limb attack angle. When running at a relatively comfortable velocity, greater leg stiffness may reflect a more energy efficient running pattern.

Time domain contact model for tyre/road interaction including nonlinear contact stiffness due to small-scale roughness

Science.gov (United States)

Andersson, P. B. U.; Kropp, W.

2008-11-01

Rolling resistance, traction, wear, excitation of vibrations, and noise generation are all attributes to consider in optimisation of the interaction between automotive tyres and wearing courses of roads. The key to understand and describe the interaction is to include a wide range of length scales in the description of the contact geometry. This means including scales on the order of micrometres that have been neglected in previous tyre/road interaction models. A time domain contact model for the tyre/road interaction that includes interfacial details is presented. The contact geometry is discretised into multiple elements forming pairs of matching points. The dynamic response of the tyre is calculated by convolving the contact forces with pre-calculated Green's functions. The smaller-length scales are included by using constitutive interfacial relations, i.e. by using nonlinear contact springs, for each pair of contact elements. The method is presented for normal (out-of-plane) contact and a method for assessing the stiffness of the nonlinear springs based on detailed geometry and elastic data of the tread is suggested. The governing equations of the nonlinear contact problem are solved with the Newton-Raphson iterative scheme. Relations between force, indentation, and contact stiffness are calculated for a single tread block in contact with a road surface. The calculated results have the same character as results from measurements found in literature. Comparison to traditional contact formulations shows that the effect of the small-scale roughness is large; the contact stiffness is only up to half of the stiffness that would result if contact is made over the whole element directly to the bulk of the tread. It is concluded that the suggested contact formulation is a suitable model to include more details of the contact interface. Further, the presented result for the tread block in contact with the road is a suitable input for a global tyre/road interaction model

Telescopic projective methods for parabolic differential equations

CERN Document Server

Gear, C W

2003-01-01

Projective methods were introduced in an earlier paper [C.W. Gear, I.G. Kevrekidis, Projective Methods for Stiff Differential Equations: problems with gaps in their eigenvalue spectrum, NEC Research Institute Report 2001-029, available from http://www.neci.nj.nec.com/homepages/cwg/projective.pdf Abbreviated version to appear in SISC] as having potential for the efficient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of stiff problems that have a large spread of eigenvalues with no gaps in their spectrum as arise in the semi-discretization of PDEs with parabolic components.

Telescopic projective methods for parabolic differential equations

International Nuclear Information System (INIS)

Gear, C.W.; Kevrekidis, Ioannis G.

2003-01-01

Projective methods were introduced in an earlier paper [C.W. Gear, I.G. Kevrekidis, Projective Methods for Stiff Differential Equations: problems with gaps in their eigenvalue spectrum, NEC Research Institute Report 2001-029, available from http://www.neci.nj.nec.com/homepages/cwg/projective.pdf Abbreviated version to appear in SISC] as having potential for the efficient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of stiff problems that have a large spread of eigenvalues with no gaps in their spectrum as arise in the semi-discretization of PDEs with parabolic components

Tailoring the mechanical properties by molecular integration of flexible and stiff polymer networks.

Science.gov (United States)

Wan, Haixiao; Shen, Jianxiang; Gao, Naishen; Liu, Jun; Gao, Yangyang; Zhang, Liqun

2018-03-28

Designing a multiple-network structure at the molecular level to tailor the mechanical properties of polymeric materials is of great scientific and technological importance. Through the coarse-grained molecular dynamics simulation, we successfully construct an interpenetrating polymer network (IPN) composed of a flexible polymer network and a stiff polymer network. First, we find that there is an optimal chain stiffness for a single network (SN) to achieve the best stress-strain behavior. Then we turn to study the mechanical behaviors of IPNs. The result shows that the stress-strain behaviors of the IPNs appreciably exceed the sum of that of the corresponding single flexible and stiff network, which highlights the advantage of the IPN structure. By systematically varying the stiffness of the stiff polymer network of the IPNs, optimal stiffness also exists to achieve the best performance. We attribute this to a much larger contribution of the non-bonded interaction energy. Last, the effect of the component concentration ratio is probed. With the increase of the concentration of the flexible network, the stress-strain behavior of the IPNs is gradually enhanced, while an optimized concentration (around 60% molar ration) of the stiff network occurs, which could result from the dominant role of the enthalpy rather than the entropy. In general, our work is expected to provide some guidelines to better tailor the mechanical properties of the IPNs made of a flexible network and a stiff network, by manipulating the stiffness of the stiff polymer network and the component concentration ratio.

Triceps-surae musculotendinous stiffness: relative differences between obese and non-obese postmenopausal women.

Science.gov (United States)

Faria, Aurélio; Gabriel, Ronaldo; Abrantes, João; Brás, Rui; Moreira, Helena

2009-12-01

There is a lack of research into the relationship between obesity and muscle-tendon unit stiffness in postmenopausal women. Muscle-tendon unit stiffness appears to affect human motion performance and excessive and insufficient stiffness can increase the risk of bone and soft tissue injuries, respectively. The aim of this study was to investigate the relationship between muscle-tendon unit stiffness and obesity in postmenopausal women. 105 postmenopausal women (58 [SD 5.5] years) participated. Four groups (normal weight, pre-obese, obesity class I and obesity class II) were defined according World Health Organization classification of body mass index. The ankle muscle-tendon unit stiffness was assessed in vivo with a free oscillation technique using a load of 30% of maximal voluntary isometric contraction. ANOVA shows significant difference in muscle-tendon unit stiffness among the groups defined (Pnormal weight-pre-obese; normal weight-obesity class I and normal weight-obesity class II. The normal weight group had stiffness of 15789 (SD 2969) N/m, pre-obese of 19971 (SD 3678) N/m, obesity class I of 21435 (SD 4295) N/m, and obesity class II of 23497 (SD 1776) N/m. Obese subjects may have increased muscle-tendon unit stiffness because of fat infiltration in leg skeletal muscles, range of motion restrictions and stability/posture reasons and might be more predisposed to develop musculoskeletal injuries. Normal weight group had identical stiffness values to those reported in studies where subjects were not yet menopausal, suggesting that stiffness might not be influenced by menopause.

A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

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Murat Osmanoglu

2013-01-01

Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.

Optimization of prosthetic foot stiffness to reduce metabolic cost and intact knee loading during below-knee amputee walking: a theoretical study.

Science.gov (United States)

Fey, Nicholas P; Klute, Glenn K; Neptune, Richard R

2012-11-01

Unilateral below-knee amputees develop abnormal gait characteristics that include bilateral asymmetries and an elevated metabolic cost relative to non-amputees. In addition, long-term prosthesis use has been linked to an increased prevalence of joint pain and osteoarthritis in the intact leg knee. To improve amputee mobility, prosthetic feet that utilize elastic energy storage and return (ESAR) have been designed, which perform important biomechanical functions such as providing body support and forward propulsion. However, the prescription of appropriate design characteristics (e.g., stiffness) is not well-defined since its influence on foot function and important in vivo biomechanical quantities such as metabolic cost and joint loading remain unclear. The design of feet that improve these quantities could provide considerable advancements in amputee care. Therefore, the purpose of this study was to couple design optimization with dynamic simulations of amputee walking to identify the optimal foot stiffness that minimizes metabolic cost and intact knee joint loading. A musculoskeletal model and distributed stiffness ESAR prosthetic foot model were developed to generate muscle-actuated forward dynamics simulations of amputee walking. Dynamic optimization was used to solve for the optimal muscle excitation patterns and foot stiffness profile that produced simulations that tracked experimental amputee walking data while minimizing metabolic cost and intact leg internal knee contact forces. Muscle and foot function were evaluated by calculating their contributions to the important walking subtasks of body support, forward propulsion and leg swing. The analyses showed that altering a nominal prosthetic foot stiffness distribution by stiffening the toe and mid-foot while making the ankle and heel less stiff improved ESAR foot performance by offloading the intact knee during early to mid-stance of the intact leg and reducing metabolic cost. The optimal design also

Betel nut chewing associated with increased risk of arterial stiffness.

Science.gov (United States)

Wei, Yu-Ting; Chou, Yu-Tsung; Yang, Yi-Ching; Chou, Chieh-Ying; Lu, Feng-Hwa; Chang, Chih-Jen; Wu, Jin-Shang

2017-11-01

Betel nut chewing is associated with certain cardiovascular outcomes. Subclinical atherosclerosis may be one link between betel nut chewing and cardiovascular risk. Few studies have examined the association between chewing betel nut and arterial stiffness. The aim of this study was thus to determine the relationship between betel nut chewing and arterial stiffness in a Taiwanese population. We enrolled 7540 eligible subjects in National Cheng Kung University Hospital from October 2006 to August 2009. The exclusion criteria included history of cerebrovascular events, coronary artery disease, and taking lipid-lowering drugs, antihypertensives, and hypoglycemic agents. Increased arterial stiffness was defined as brachial-ankle pulse wave velocity (baPWV) ≥1400cm/s. According to their habit of betel nut use, the subjects were categorized into non-, ex-, and current chewers. The prevalence of increased arterial stiffness was 32.7, 43.3, and 43.2% in non-, ex- and current chewers, respectively (p=0.011). Multiple logistic regression analysis revealed that ex-chewers (odds ratio [OR] 1.69, 95% confidence interval (CI)=1.08-2.65) and current chewers (OR 2.29, 95% CI=1.05-4.99) had elevated risks of increased arterial stiffness after adjustment for co-variables. Both ex- and current betel nut chewing were associated with a higher risk of increased arterial stiffness. Stopping betel nut chewing may thus potentially be beneficial to reduce cardiovascular risk, based on the principals of preventive medicine. Copyright © 2017 Elsevier B.V. All rights reserved.

Sex Differences in Limb and Joint Stiffness in Recreational Runners

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Sinclair Jonathan

2015-09-01

Full Text Available Purpose. Female runners are known to be at greater risk from chronic running injuries than age-matched males, although the exact mechanisms are often poorly understood. The aim of the current investigation was to determine if female recreational runners exhibit distinct limb and joint stiffness characteristics in relation to their male counterparts. Methods. Fourteen male and fourteen female runners ran over a force platform at 4.0 m · s-1. Lower limb kinematics were collected using an eight-camera optoelectric motion capture system operating at 250 Hz. Measures of limb and joint stiffness were calculated as a function of limb length and joint moments divided by the extent of limb and joint excursion. All stiffness and joint moment parameters were normalized to body mass. Sex differences in normalized limb and knee and ankle joint stiffness were examined statistically using independent samples t tests. Results. The results indicate that normalized limb (male = 0.18 ± 0.07, female = 0.37 ± 0.10 kN · kg · m-1 and knee stiffness (male = 5.59 ± 2.02, female = 7.34 ± 1.78 Nm · kg · rad-1 were significantly greater in female runners. Conclusions. On the basis that normalized knee and limb stiffness were shown to be significantly greater in female runners, the findings from the current investigation may provide further insight into the aetiology of the distinct injury patterns observed between sexes.

A numerical method for solving singular De`s

Energy Technology Data Exchange (ETDEWEB)

Mahaver, W.T.

1996-12-31

A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.

Measurable Strategies in Differential Games

Science.gov (United States)

Ivanov, R. P.

1990-02-01

Nonlinear approach-evasion differential games are considered in which the initial data depend on the time. These games are investigated in the class of strategies that are functions of three variables, namely, the time, the phase variable, and the current value of the other player's control, and are measurable jointly with respect to the time and the phase variable. The ideas of the Pontryagin methods in differential games and Krasovskiĭ's ideas on extremal aiming are developed, and it is shown that measurable strategies have broad applicability. It is proved that measurable strategies are compatible with differential equations with discontinuous right-hand side, and general theorems on the existence of solving measurable strategies in approach-evasion problems are proved, along with some auxiliary assertions. It is shown that the saddle point condition in the small game ensures the existence of solving measurable strategies. An example is given. Bibliography: 14 titles.

Stiff-Person Syndrome and Graves’ Disease

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Lais Moreira Medeiros MD

2016-12-01

Full Text Available A 9-year-old female child presented with a history of falls, weight loss, diffuse leg pain, and progressive gait disorder, following 1 previous event described as a tonic–clonic seizure. She had increased thyroid volume, brisk symmetric reflexes, abnormal gait, and painful spasms of the paraspinal musculature. Thyroid function tests indicated biochemical hyperthyroidism, and thyrotropin receptor antibodies were positive. Her electromyography showed continuous activation of normal motor units of the paraspinal and proximal lower extremity muscles. The patient had a diagnosis of Graves’ disease with associated stiff-person syndrome, with elevated anti–glutamic acid decarboxylase antibody levels. After intravenous immunoglobulin therapy, her ambulation was substantially improved and the symptoms of stiff-person syndrome decreased dramatically.

Hormones and arterial stiffness in patients with chronic kidney disease.

Science.gov (United States)

Gungor, Ozkan; Kircelli, Fatih; Voroneanu, Luminita; Covic, Adrian; Ok, Ercan

2013-01-01

Cardiovascular disease constitutes the major cause of mortality in patients with chronic kidney disease. Arterial stiffness is an important contributor to the occurrence and progression of cardiovascular disease. Various risk factors, including altered hormone levels, have been suggested to be associated with arterial stiffness. Based on the background that chronic kidney disease predisposes individuals to a wide range of hormonal changes, we herein review the available data on the association between arterial stiffness and hormones in patients with chronic kidney disease and summarize the data for the general population.

Cellular shear stiffness reflects progression of arsenic-induced transformation during G1

DEFF Research Database (Denmark)

Muñoz, Alexandra; Eldridge, Will J; Jakobsen, Nina Munkholt

2017-01-01

epithelial cells were exposed to sodium arsenite to initiate early stages of transformation. Exposed cells were cultured in soft agar to further transformation and select for clonal populations exhibiting anchorage independent growth. Shear stiffness of various cell populations in G1 was assessed using...... reduced stiffness relative to control clonal lines, which were cultured in soft agar but did not receive arsenic treatment. The relative standard deviation of the stiffness of Arsenic clones was reduced compared to control clones, as well as to the arsenic exposed cell population. Cell stiffness...

Research on a novel high stiffness axial passive magnetic bearing for DGMSCMG

International Nuclear Information System (INIS)

Sun, Jinji; Wang, Chun'e; Le, Yun

2016-01-01

To increase the displacement stiffness and decrease power loss of double gimbals magnetically suspended control momentum gyro (DGMSCMG), this paper researches a new structure of axial passive magnetic bearing (APMB). Different from the existing APMB, the proposed APMB is composed of segmented permanent magnets and magnetic rings. The displacement stiffness and angular stiffness expressions are derived by equivalent magnetic circuit method and infinitesimal method based on the end magnetic flux. The relationships are analyzed between stiffness and structure parameters such as length of air gap, length of permanent magnet, height of permanent magnet and end length of magnetic ring. Besides, the axial displacement stiffness measurement method of the APMB is proposed, and it verified the correctness of proposed theoretical method. The DGMSCMG prototype is manufactured and the slow-down characteristic experiment is carried out, and the experimental result reflects the low power loss feature of the APMB. - Highlights: • A novel high stiffness axial passive magnetic bearing for DGMSCMG. • The proposed APMB is composed of segmented permanent magnets and magnetic rings. • The APMB is analyzed by EMCM and infinitesimal method based on the end magnetic flux. • The axial displacement stiffness measurement method of the APMB is proposed. • The DGMSCMG is manufactured and proved the correctness of theoretical analysis.

Theoretical and experimental studies on in-plane stiffness of integrated container structure

Directory of Open Access Journals (Sweden)

Xiaoxiong Zha

2016-03-01

Full Text Available This article presents analytical, numerical, and experimental studies on the in-plane stiffness of container buildings. First, based on diaphragm theory, parallel corrugated direction stiffness of corrugated sheet has been deduced, and based on energy method, shear modulus of two elastic principal directions of orthotropic plate has been deduced, and through stiffness conversion method, the stiffness relationship between parallel corrugated direction and vertical corrugated direction has been obtained. Combined with container frame, the container stiffness of loading end and non-loading end, as bottom side beam fixed, has been obtained. Second, through the software Abaqus, full-scale container model has been established. The loading–displacement curve of finite element model has been compared with theoretical analysis and has a good agreement. Third, through 20 and 40 ft container, corresponding experimental verification has been done, and by comparison of container stiffness, the theoretical analysis and finite element simulation have been verified. Finally, based on verified finite element model, parametric analysis of corrugated sheet size, corrugated sheeting cross section, elasticity modulus of top side beam, and every plate action for container stiffness have been given. Research result has made feasible in design and construction of container buildings and can provide some references to corresponding specification preparation.

Corporate Leverage and Product Differentiation Strategy

OpenAIRE

Arping, Stefan; Lóránth, Gyöngyi

2002-01-01

This article develops a model of the interplay between corporate leverage and product differentiation strategy. Leverage improves managerial discipline, but it can also raise customer concerns about a vendor's long-term viability. We argue that customer concerns about firm viability will be particularly pronounced when products are highly differentiated from competitors' products. In this context, optimal product differentiation strategies solve a trade-off between softening price competition...

Human arm stiffness and equilibrium-point trajectory during multi-joint movement.

Science.gov (United States)

Gomi, H; Kawato, M

1997-03-01

By using a newly designed high-performance manipulandum and a new estimation algorithm, we measured human multi-joint arm stiffness parameters during multi-joint point-to-point movements on a horizontal plane. This manipulandum allows us to apply a sufficient perturbation to subject's arm within a brief period during movement. Arm stiffness parameters were reliably estimated using a new algorithm, in which all unknown structural parameters could be estimated independent of arm posture (i.e., constant values under any arm posture). Arm stiffness during transverse movement was considerably greater than that during corresponding posture, but not during a longitudinal movement. Although the ratios of elbow, shoulder, and double-joint stiffness were varied in time, the orientation of stiffness ellipses during the movement did not change much. Equilibrium-point trajectories that were predicted from measured stiffness parameters and actual trajectories were slightly sinusoidally curved in Cartesian space and their velocity profiles were quite different from the velocity profiles of actual hand trajectories. This result contradicts the hypothesis that the brain does not take the dynamics into account in movement control depending on the neuromuscular servo mechanism; rather, it implies that the brain needs to acquire some internal models of controlled objects.

Sabot Front Borerider Stiffness vs. Dispersion: Finding the Knee in the Curve

Directory of Open Access Journals (Sweden)

Alan F. Hathaway

2001-01-01

Full Text Available In the design of armor piercing, fin-stabilized, discarding sabot projectiles, the radial stiffness of the sabot front borerider has a significant impact on the projectile's dispersion and is, therefore, an important design consideration. Whether designing a new projectile or trying to improve an existing design, projectile designers can achieve front borerider stiffness without understanding its affect on dispersion characteristics. There is a knee in the stiffness vs. dispersion curve at which a change in the sabot front borerider stiffness will have a significant impact on dispersion or no impact at all depending on whether the stiffness is increased or decreased. The subject of this paper is an analytical approach to quantitatively determine the knee in the curve. Results from using this approach on the M865 APFSDS projectile are also presented.

Knee joint stiffness in individuals with and without knee osteoarthritis: a preliminary study.

Science.gov (United States)

Oatis, Carol A; Wolff, Edward F; Lennon, Sandra K

2006-12-01

Descriptive, case-matched comparison. To compare the knee joint stiffness and damping coefficients of individuals with knee osteoarthritis (KOA) to those of age- and gender-matched individuals without KOA. A secondary purpose was to investigate relationships between these coefficients and complaints of stiffness in individuals with KOA. KOA is a leading cause of disability, and stiffness is a common complaint in individuals with KOA. Yet the most common method of assessing knee joint stiffness is through a self-report questionnaire. Stiffness and damping coefficients at the knee were calculated in 10 volunteers (mean age +/- SD, 64.1+/-15.5 years) with KOA and compared to coefficients from age-and gender-matched individuals without KOA, collected in a previous study (mean age +/- SD, 62.1+/-13.9 years). Stiffness and damping coefficients were calculated from the angular motion of the knee during a relaxed oscillation. Spearman correlation coefficients were calculated between stiffness and damping coefficients and WOMAC (Western Ontario and McMaster Universities Osteoarthritis Index) scores for subjects with KOA. Independent 2-tailed t tests revealed significantly larger damping coefficients (P = .035) among those with KOA (95% CI, 0.10-2.32 Nm s/rad). Spearman rank correlations revealed a significant positive relationship (r = .85, P = .003) between the damping coefficient and the stiffness subscore of the WOMAC. This study offers preliminary data demonstrating the feasibility of measuring stiffness and damping coefficients in individuals with KOA. Additionally, the damping coefficient is increased in people with KOA when compared to age- and gender-matched individuals without KOA. The damping coefficient appears to be associated with the complaints of stiffness reported by the WOMAC.

Evaluation of stiffness feedback for hard nodule identification on a phantom silicone model.

Science.gov (United States)

Li, Min; Konstantinova, Jelizaveta; Xu, Guanghua; He, Bo; Aminzadeh, Vahid; Xie, Jun; Wurdemann, Helge; Althoefer, Kaspar

2017-01-01

Haptic information in robotic surgery can significantly improve clinical outcomes and help detect hard soft-tissue inclusions that indicate potential abnormalities. Visual representation of tissue stiffness information is a cost-effective technique. Meanwhile, direct force feedback, although considerably more expensive than visual representation, is an intuitive method of conveying information regarding tissue stiffness to surgeons. In this study, real-time visual stiffness feedback by sliding indentation palpation is proposed, validated, and compared with force feedback involving human subjects. In an experimental tele-manipulation environment, a dynamically updated color map depicting the stiffness of probed soft tissue is presented via a graphical interface. The force feedback is provided, aided by a master haptic device. The haptic device uses data acquired from an F/T sensor attached to the end-effector of a tele-manipulated robot. Hard nodule detection performance is evaluated for 2 modes (force feedback and visual stiffness feedback) of stiffness feedback on an artificial organ containing buried stiff nodules. From this artificial organ, a virtual-environment tissue model is generated based on sliding indentation measurements. Employing this virtual-environment tissue model, we compare the performance of human participants in distinguishing differently sized hard nodules by force feedback and visual stiffness feedback. Results indicate that the proposed distributed visual representation of tissue stiffness can be used effectively for hard nodule identification. The representation can also be used as a sufficient substitute for force feedback in tissue palpation.

Evaluation of stiffness feedback for hard nodule identification on a phantom silicone model.

Directory of Open Access Journals (Sweden)

Min Li

Full Text Available Haptic information in robotic surgery can significantly improve clinical outcomes and help detect hard soft-tissue inclusions that indicate potential abnormalities. Visual representation of tissue stiffness information is a cost-effective technique. Meanwhile, direct force feedback, although considerably more expensive than visual representation, is an intuitive method of conveying information regarding tissue stiffness to surgeons. In this study, real-time visual stiffness feedback by sliding indentation palpation is proposed, validated, and compared with force feedback involving human subjects. In an experimental tele-manipulation environment, a dynamically updated color map depicting the stiffness of probed soft tissue is presented via a graphical interface. The force feedback is provided, aided by a master haptic device. The haptic device uses data acquired from an F/T sensor attached to the end-effector of a tele-manipulated robot. Hard nodule detection performance is evaluated for 2 modes (force feedback and visual stiffness feedback of stiffness feedback on an artificial organ containing buried stiff nodules. From this artificial organ, a virtual-environment tissue model is generated based on sliding indentation measurements. Employing this virtual-environment tissue model, we compare the performance of human participants in distinguishing differently sized hard nodules by force feedback and visual stiffness feedback. Results indicate that the proposed distributed visual representation of tissue stiffness can be used effectively for hard nodule identification. The representation can also be used as a sufficient substitute for force feedback in tissue palpation.

Cryotherapy induces an increase in muscle stiffness.

Science.gov (United States)

Point, M; Guilhem, G; Hug, F; Nordez, A; Frey, A; Lacourpaille, L

2018-01-01

Although cold application (ie, cryotherapy) may be useful to treat sports injuries and to prevent muscle damage, it is unclear whether it has adverse effects on muscle mechanical properties. This study aimed to determine the effect of air-pulsed cryotherapy on muscle stiffness estimated using ultrasound shear wave elastography. Myoelectrical activity, ankle passive torque, shear modulus (an index of stiffness), and muscle temperature of the gastrocnemius medialis were measured before, during an air-pulsed cryotherapy (-30°C) treatment of four sets of 4 minutes with 1-minute recovery in between and during a 40 minutes postcryotherapy period. Muscle temperature significantly decreased after the second set of treatment (10 minutes: 32.3±2.5°C; Pcryotherapy induces an increase in muscle stiffness. This acute change in muscle mechanical properties may lower the amount of stretch that the muscle tissue is able to sustain without subsequent injury. This should be considered when using cryotherapy in athletic practice. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

The relationship between passive stiffness and evoked twitch properties: the influence of muscle CSA normalization

International Nuclear Information System (INIS)

Ryan, E D; Thompson, B J; Sobolewski, E J; Herda, T J; Costa, P B; Walter, A A; Cramer, J T

2011-01-01

Passive stiffness measurements are often used as a clinical tool to examine a muscle's passive lengthening characteristics. The purpose of this study was to examine the relationship between passive stiffness and evoked twitch properties prior to and following normalization of passive stiffness to muscle cross-sectional area (CSA). Ten healthy volunteers (mean ± SD age = 23 ± 3 year) performed passive range of motion, evoked twitch, and muscle CSA assessments of the plantar flexor muscles. Passive stiffness was determined from the slope of the final 5° of the angle–torque curve. Peak twitch torque (PTT) and rate of torque development (RTD) were determined via transcutaneous electrical stimulation, and muscle CSA was assessed using a peripheral quantitative computed tomography scanner. Pearson product moment correlation coefficients (r) were used to assess the relationships between passive stiffness and PTT and RTD and normalized passive stiffness (passive stiffness . muscle CSA −1 ) and PTT and RTD. Significant positive relationships were observed between passive stiffness and PTT (P = 0.003, r = 0.828) and RTD (P = 0.003, r = 0.825). There were no significant relationships between normalized passive stiffness and PTT (P = 0.290, r = 0.372) or RTD (P = 0.353, r = 0.329) demonstrating that stiffness did not account for a significant portion of the variance in twitch properties. Passive stiffness was largely influenced by the amount of muscle tissue in this study. Future studies that examine muscle stiffness and its relationship with performance measures, among different populations, and following various interventions may consider normalizing stiffness measurements to muscle CSA

GDTM-Padé technique for the non-linear differential-difference equation

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Lu Jun-Feng

2013-01-01

Full Text Available This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.

Stiffness Analysis and Comparison of 3-PPR Planar Parallel Manipulators with Actuation Compliance

DEFF Research Database (Denmark)

Wu, Guanglei; Bai, Shaoping; Kepler, Jørgen Asbøl

2012-01-01

In this paper, the stiffness of 3-PPR planar parallel manipulator (PPM) is analyzed with the consideration of nonlinear actuation compliance. The characteristics of the stiffness matrix pertaining to the planar parallel manipulators are analyzed and discussed. Graphic representation of the stiffn...... of the stiffness characteristics by means of translational and rotational stiffness mapping is developed. The developed method is illustrated with an unsymmetrical 3-PPR PPM, being compared with its structure-symmetrical counterpart....

Role of flexural stiffness of leukocyte microvilli in adhesion dynamics

Science.gov (United States)

Wu, Tai-Hsien; Qi, Dewei

2018-03-01

Previous work reported that microvillus deformation has an important influence on dynamics of cell adhesion. However, the existing studies were limited to the extensional deformation of microvilli and did not consider the effects of their bending deformation on cell adhesion. This Rapid Communication investigates the effects of flexural stiffness of microvilli on the rolling process related to adhesion of leukocytes by using a lattice-Boltzmann lattice-spring method (LLM) combined with adhesive dynamics (AD) simulations. The simulation results reveal that the flexural stiffness of microvilli and their bending deformation have a profound effect on rolling velocity and adhesive forces. As the flexural stiffness of the microvilli decreases, their bending angles increase, resulting in an increase in the number of receptor-ligand bonds and adhesive bonding force and a decrease in the rolling velocity of leukocytes. The effects of flexural stiffness on deformation and adhesion represent crucial factors involved in cell adhesion.

Differential equations problem solver

CERN Document Server

Arterburn, David R

2012-01-01

REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

Evaluation of arterial stiffness in nondiabetic chronic kidney disease patients

Directory of Open Access Journals (Sweden)

Bodanapu Mastanvalli

2017-01-01

Full Text Available Chronic kidney disease (CKD is a growing problem worldwide. Clinical and epidemiologic studies have shown that structural and functional changes that occur in major arteries are a major contributing factor to the high mortality in uremic patients. Recent studies have shown a stepwise increase of the carotid-femoral pulse wave velocity (cfPWV from CKD Stage 1 to Stage 5. We evaluated the cfPWV and augmentation index (AIx, as indirect markers of arterial stiffness in patients with nondiabetic CKD and compared the values with normal population; we also evaluated the relationship between various stages of CKD and arterial stiffness markers. This cross-sectional study was carried out in the Department of Nephrology for a duration of two years from January 15, 2012, to January 14, 2014. Fifty patients with nondiabetic CKD were studied along with 50 healthy volunteers who did not have CKD, who served as controls. Assessment of arterial stiffness (blood pressure, PWV, heart rate, aortic augmentation pressure, and AIx was performed using the PeriScope device. PWV positively correlated with systolic and diastolic blood pressure, mean aortic arterial pressure, serum creatinine, and serum uric acid and negatively correlated with estimated glomerular filtration rate. Arterial stiffness increased as CKD stage increased and was higher in nondiabetic CKD group than in the general population. Arterial stiffness progressed gradually from CKD Stage 2 to 5, and then abruptly, in dialysis patients. Measures to decrease the arterial stiffness and its influence on decreasing cardiovascular events need further evaluation.

Exp-function method for solving fractional partial differential equations.

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Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Vascular Stiffness and Increased Pulse Pressure in the Aging Cardiovascular System

Directory of Open Access Journals (Sweden)

Jochen Steppan

2011-01-01

Full Text Available Aging leads to a multitude of changes in the cardiovascular system, including systolic hypertension, increased central vascular stiffness, and increased pulse pressure. In this paper we will review the effects of age-associated increased vascular stiffness on systolic blood pressure, pulse pressure, augmentation index, and cardiac workload. Additionally we will describe pulse wave velocity as a method to measure vascular stiffness and review the impact of increased vascular stiffness as an index of vascular health and as a predictor of adverse cardiovascular outcomes. Furthermore, we will discuss the underlying mechanisms and how these may be modified in order to change the outcomes. A thorough understanding of these concepts is of paramount importance and has therapeutic implications for the increasingly elderly population.

One-loop potential in the new string model with negative stiffness

International Nuclear Information System (INIS)

Kleinert, H.; Chervyakov, A.M.; Nesterenko, V.V.

1996-01-01

The color-electric flux tube between quarks has a finite thickness therefore also a finite curvature stiffness. Contrary to earlier rigid-string proposal by Polyakov and Kleinert and motivated by the properties of a magnetic flux tube in a type-II superconductor, we put forward the hypothesis that the stiffness is negative. We set up and study the properties of an idealized string model with such negative stiffness. In contrast to the rigid string, the propagator in the new model has no unphysical pole. One-loop calculations show that the model generates an interquark potential which does not contain the square root singularity even for moderate values of a negative stiffness. At large distances, the potential has usual linearly rising term with the universal Luescher correction

MINIMUM BRACING STIFFNESS FOR MULTI-COLUMN SYSTEMS: THEORY

OpenAIRE

ARISTIZÁBAL-OCHOA, J. DARÍO

2011-01-01

A method that determines the minimum bracing stiffness required by a multi-column elastic system to achieve non-sway buckling conditions is proposed. Equations that evaluate the required minimum stiffness of the lateral and torsional bracings and the corresponding “braced" critical buckling load for each column of the story level are derived using the modified stability functions. The following effects are included: 1) the types of end connections (rigid, semirigid, and simple); 2) the bluepr...

Ordinary differential equation for local accumulation time.

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Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

Convergence of hybrid methods for solving non-linear partial ...

African Journals Online (AJOL)

This paper is concerned with the numerical solution and convergence analysis of non-linear partial differential equations using a hybrid method. The solution technique involves discretizing the non-linear system of PDE to obtain a corresponding non-linear system of algebraic difference equations to be solved at each time ...

The effect of eccentric and concentric calf muscle training on Achilles tendon stiffness.

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Morrissey, Dylan; Roskilly, Anna; Twycross-Lewis, Richard; Isinkaye, Tomide; Screen, Hazel; Woledge, Roger; Bader, Dan

2011-03-01

To compare in vivo effects of eccentric and concentric calf muscle training on Achilles tendon stiffness, in subjects without tendinopathy. Thirty-eight recreational athletes completed 6 weeks eccentric (6 males, 13 females, 21.6  ±  2.2 years) or concentric training (8 males, 11 females, 21.1  ±  2.0 years). Achilles tendon stiffness, tendon modulus and single-leg jump height were measured before and after intervention. Exercise adherence was recorded using a diary. All data are reported as mean  ±  SD. Groups were matched for height and weight but the eccentric training group were more active at baseline (P Tendon stiffness was higher in the eccentrically trained group at baseline compared to the concentrically trained group (20.9  ±  7.3 N/mm v 13.38  ±  4.66 N/mm; P = 0.001) and decreased significantly after eccentric training (to 17.2 ( ±  5.9) N/mm (P = 0.035)). There was no stiffness change in the concentric group (P = 0.405). Stiffness modulus showed similar changes to stiffness. An inverse correlation was found between initial, and subsequent, reduction in stiffness (r = -0.66). Jump height did not change and no correlation between stiffness change and adherence was observed in either group (r = 0.01). Six weeks of eccentric training can alter Achilles tendon stiffness while a matched concentric programme shows no similar effects. Studies in patients with Achilles tendinopathy are warranted.

Hypertension, Diabetes Type II, and Their Association: Role of Arterial Stiffness.

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Smulyan, Harold; Lieber, Ari; Safar, Michel E

2016-01-01

In patients with both hypertension and type II diabetes, the systolic blood pressure (SBP) increases linearly with age, while that of diastolic blood pressure (DBP) declines curvilinearly as early as age 45, all suggesting the development of increased arterial stiffness. Increased stiffness is an important, independent, and significant risk predictor in subjects with hypertension and diabetes. In patients with both diseases, stiffness assessed at the same mean arterial pressure (MAP) was significantly higher in diabetic patients. Arterial stiffness is related to age, heart rate (HR), and MAP, but in diabetic patients, it also related to diabetes duration and insulin treatment (IT). In the metabolic syndrome (MetSyn), diabetes also acts on the small arteries through capillary rarefaction to reduce the effective length of the arterial tree, increases the reflected pulse wave and thus the pulse pressure (PP). These studies indicate that diabetes and hypertension additively contribute to increased pulsatility and suggest that any means to reduce stiffness would be beneficial in these conditions. © American Journal of Hypertension, Ltd 2015. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Matrix Stiffness Corresponding to Strictured Bowel Induces a Fibrogenic Response in Human Colonic Fibroblasts

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Johnson, Laura A.; Rodansky, Eva S.; Sauder, Kay L.; Horowitz, Jeffrey C.; Mih, Justin D.; Tschumperlin, Daniel J.; Higgins, Peter D.

2013-01-01

Background Crohn’s disease is characterized by repeated cycles of inflammation and mucosal healing which ultimately progress to intestinal fibrosis. This inexorable progression towards fibrosis suggests that fibrosis becomes inflammation-independent and auto-propagative. We hypothesized that matrix stiffness regulates this auto-propagation of intestinal fibrosis. Methods The stiffness of fresh ex vivo samples from normal human small intestine, Crohn’s disease strictures, and the unaffected margin were measured with a microelastometer. Normal human colonic fibroblasts were cultured on physiologically normal or pathologically stiff matrices corresponding to the physiological stiffness of normal or fibrotic bowel. Cellular response was assayed for changes in cell morphology, α-smooth muscle actin (αSMA) staining, and gene expression. Results Microelastometer measurements revealed a significant increase in colonic tissue stiffness between normal human colon and Crohn’s strictures as well as between the stricture and adjacent tissue margin. In Ccd-18co cells grown on stiff matrices corresponding to Crohn’s strictures, cellular proliferation increased. Pathologic stiffness induced a marked change in cell morphology and increased αSMA protein expression. Growth on a stiff matrix induced fibrogenic gene expression, decreased matrix metalloproteinase and pro-inflammatory gene expression, and was associated with nuclear localization of the transcriptional cofactor MRTF-A. Conclusions Matrix stiffness, representative of the pathological stiffness of Crohn’s strictures, activates human colonic fibroblasts to a fibrogenic phenotype. Matrix stiffness affects multiple pathways suggesting the mechanical properties of the cellular environment are critical to fibroblast function and may contribute to autopropagation of intestinal fibrosis in the absence of inflammation, thereby contributing to the intractable intestinal fibrosis characteristic of Crohn’s disease. PMID

Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities